Adrian Constantin, Boris Kolev
Pages: 471 - 474
For an integrable shallow water equation we describe a geometrical approach shoing that any two nearby fluid configurations are successive states of a unique flow minimizing the kinetic energy.
K. Kobayashi, H. Okamoto
Pages: 472 - 479
We consider two-dimensional water-waves of permanent shape with a constant proagation speed. Two theorems concerning the uniqueness of certain solutions are rported. Uniqueness of Crapper's pure capillary waves is proved under a positivity assumption. The proof is based on the theory of positive operators....
Peng Zhao, Engui Fan, Temuerchaolu
Pages: 468 - 482
We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebrogeometric method. Our main tools include algebraic curve and Riemann surface, polynomial recursive formulation and a special meromorphic function.
Pages: 469 - 472
A novel, remarkably neat, differential algorithm is introduced, which is suitable to evaluate all the zeros of a generic polynomial of arbitrary degree N.
Pages: 469 - 474
A system of algebraic equations satisfied by the zeros of the sum of three polynomials are reported.
Dimitrios A. Pinotsis
Pages: 474 - 493
We show that by deforming the Riemann-Hilbert (RH) formalism associated with certain linear PDEs and using the so-called dressing method, it is possible to derive in an algorithmic way nonlinear integrable versions of these equations. In the usual Dressing Method, one first postulates a matrix RH problem...
Pages: 474 - 477
By means of splitting subgroups of the generalized Poincaré group P(1, 4), ansatzes which reduce the eikonal equation to differential equations with fewer independent variables have been constructed. The corresponding symmetry reduction has been done. By means of the solutions of the reduced equations...
Ayse Karasu (Kalkanli), Hasan Yildirim
Pages: 475 - 482
In this work, we study the Lie-point symmetries of KeplerErmakov systems presented by C Athorne in J. Phys. A24 (1991), L1385L1389. We determine the forms of arbitrary function H(x, y) in order to find the members of this class possessing the sl(2, R) symmetry and a Lagrangian. We show that these systems...
Atsuo Kuniba, Masato Okado, Yasuhiko Yamada
Pages: 475 - 507
A soliton cellular automaton on a one dimensional semi-infinite lattice with a reflecting end is presented. It extends a box-ball system on an infinite lattice associated with the crystal base of Uq(sln). A commuting family of time evolutions are obtained by adapting the K matrices and the double row...
P.G.L. Leach, M.C. Nucci, S. Cotsakis
Pages: 475 - 490
We show that the concept of complete symmetry group introduced by Krause (J. Math. Phys. 35 (1994), 57345748) in the context of the Newtonian Kepler problem has wider applicability, extending to the relativistic context of the Einstein equations dscribing spherically symmetric bodies with certain conformal...
Jaume Llibre, Regilene Oliveira, Claudia Valls
Pages: 473 - 494
In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. In this paper we study the opposite to its chaotic motion, i.e. its integrability,...
Yu Hou, Engui Fan
Pages: 473 - 508
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through an algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism, the hyperelliptic...
Pages: 478 - 480
We describe a class of generalized gas dynamics equations invariant under the extended Galilei algebra A ~G(1, n).
Mario Bruschi, Francesco Calogero
Pages: 474 - 485
(z; t) be a (monic) time-dependent polynomial of arbitrary degree N in z, and let zn ≡ zn (t) be its N zeros:
. In this paper we report a convenient expression of the k-th time-derivative
of the zero zn (t). This formula plays a key role in the...
Pages: 474 - 474
Pages: 479 - 483
In this paper, we get an asymptotic expansion of the q-gamma function q(x). Also, we deduced q-analogues of Gauss' multiplication formula and Legendre's relation which give the known results when q tends to 1.
R. S. Johnson
Pages: 475 - 493
We describe a problem that can be tackled more-or-less routinely using the ideas of classical fluid mechanics, but it is a complex flow and even the linearised problem involves considerable algebraic complexity. The presentation here emphasises the approach that we adopt in order to formulate an accessible...
Guillaume Chèze, Thomas Cluzeau
Pages: 475 - 479
We consider generalized Liénard polynomial differential systems of the form ẋ = y, ẏ = -g(x) - f (x) y, with f (x) and g(x) two polynomials satisfying deg(g) ≤ deg(f). In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In...
Pages: 475 - 482
A central hyperplane arrangement in ℂ2 with multiplicity is called a “locus configuration” if it satisfies a series of “locus equations” on each hyperplane. Following , we demonstrate that the first locus equation for each hyperplane corresponds to a force-balancing equation on a related interacting...
Pages: 480 - 481
We show that the free Schrödinger equation admits Lorentz space-time transformations when corresponding transformations of the -function are nonlocal. Some consequences of this symmetry are discussed.
T.A. Ivanova, A.D. Popov
Pages: 480 - 494
We describe constructing solutions of the field equations of Chern-Simons and toplogical BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries...
Pages: 480 - 498
The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism...
Jaume Llibre, Claudia Valls
Pages: 477 - 488
In this paper we study the integrability of the Muthuswamy–Chua system
For α = 0 we characterize all its generalized rational first integrals, which contains the Darboux type first integrals. For α ≠ 0 we show that the system has no Darboux type first...
Lyudmyla L. Barannyk
Pages: 482 - 491
Solutions invariant under subalgebras of the affine algebra AIGL(3, R) are found.
Fabio Musso, Matteo Petrera, Orlando Ragnisco
Pages: 482 - 498
We perform a InönüWigner contraction on Gaudin models, showing how the integrbility property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the same linear r-matrix structure. We give a general construction...
Pages: 478 - 493
We study solutions of the KdV equation governed by a stationary equation for symmetries from the non-commutative subalgebra, namely, for a linear combination of the master-symmetry and the scaling symmetry. The constraint under study is equivalent to a sixth order nonautonomous ODE possessing two first...
Boris A. Kupershmidt
Pages: 483 - 495
Abstract telegrapher's equations and some random walks of Poisson type are shown to fit into the framework of the Hamiltonian formalism after an appropriate timedependent rescaling of the basic variables has been made.
F. Calogero, M. Sommacal
Pages: 483 - 516
In a previous paper the real evolution of the system of ODEs ¨zn + zn = N m=1, m=n gnm(zn - zm) -3 , zn zn(t), zn dzn(t) dt , n = 1, . . . , N is discussed in CN , namely the N dependent variables zn, as well as the N(N - 1) (arbitrary!) "coupling constants" gnm, are considered to be complex numbers,...
Pages: 484 - 491
We consider a symmetric, steady, and periodic water wave. It is shown that a locally vanishing vertical velocity component implies a flat or oscillating surface profile.
Fethi Bouzeffour, Ali Zagouhani
Pages: 480 - 494
In this paper we express the matrix coefficients of the Fock representation of a q-oscillator algebra in terms of the d-orthogonal Al-Salam Carlitz polynomials. Also, we derive a generating functions, recurrence relations and q-difference equations for these d-orthogonal polynomials.
Pages: 487 - 525
We present a notation for q-calculus, which leads to a new method for computtions and classifications of q-special functions. With this notation many formulas of q-calculus become very natural, and the q-analogues of many orthogonal polynomals and functions assume a very pleasant form reminding directly...
Qi Li, Wen Zhang, Qiu-Yuan Duan, Deng-Yuan Chen
Pages: 483 - 490
It is shown that the AKNS hierarchy with self-consistent sources can transform to KN hierarchy with self-consistent sources through a transformation operator and gauge transformation. Besides, there exists transformation in their conservation laws and Hamiltonian structures.
Boling Guo, Nan Liu
Pages: 483 - 508
We derive the long-time asymptotics for the solution of initial-boundary value problem of coupled nonlinear Schrödinger equation whose Lax pair involves 3 × 3 matrix in present paper. Based on a nonlinear steepest descent analysis of an associated 3 × 3 matrix Riemann–Hilbert problem, we can give the...
M. C. Nucci, P. G. L. Leach
Pages: 485 - 490
We present an equation of the fourth-order which does not possess a second-order Lagrangian and demonstrate by means of the method of reduction of order that one can obtain a first-order Lagrangian for it. This opens the way to quantization through the construction of an Hamiltonian which is suitable...
S.E. Konstein, I.V. Tyutin
Pages: 485 - 496
Symplectic reflection algebra H1,η(G) has a T(G)-dimensional space of traces whereas, when considered as a superalgebra with a natural parity, it has an S(G)-dimensional space of supertraces. The values of T(G) and S(G) depend on the symplectic reflection group G and do not depend on the parameter η.
Pages: 486 - 493
New solvable dynamical systems are identified and the properties of their solutions are tersely discussed.
G.B. Malykin, V.I. Pozdnyakova, I.A. Shereshevskii
Pages: 491 - 517
We propose a new approach to the mathematical description of light propagation in a single-mode fiber light-guide (SMFLG) with random inhomogeneities. We investgate statistics of complex amplitudes of the electric field of light wave by methods of the random group theory. We have analyzed the behavior...
A.N. Vall, S.E. Korenblit, V.M. Leviant, A.B. Tanaev
Pages: 492 - 503
Exact solutions of Heisenberg equations and two-particle eigenvalue problems for the nonrelativistic four-fermion interaction and N, model are obtained in the framework of a dynamical mapping method. Equivalence of different dynamical mappings is shown.
Ahmed Fitouhi, Néji Bettaibi
Pages: 492 - 506
This paper aims to study the q-wavelets and the q-wavelet transforms, using only the q-Jackson integrals and the q-cosine Fourier transform, for a fix q ]0, 1[. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.
Dong Gong, Xianguo Geng
Pages: 489 - 523
On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the relativistic Toda hierarchy are straightened out using the Abel–Jacobi coordinates. The meromorphic function and the Baker–Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions...
Norbert Euler, Marianna Euler
Pages: 489 - 504
We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal...
Pages: 494 - 526
We study the 'q-> infinite' limit of the q-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation rela- tions of the 'q -> infinite' current algebra are underlied by certain affine Poisson structure on the group of holomorphic maps from the...
Pages: 495 - 510
Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order symmetries, recursion operators and hierarchies of conservation...
Utpal Roy, Thokala Soloman Raju, Prasanta K. Panigrahi, Ashutosh Rai
Pages: 491 - 499
We obtain spikes or extremely short pulses for reduced Maxwell-Duffing equations under a general boundary condition, connecting the electric field and electron amplitude, using a Möbius transformation. For a nonzero background, this system is shown to admit two families of exact solutions in the form...
Shou-Fu Tian, Hong-Qing Zhang
Pages: 491 - 502
In this letter, the two-singular-manifold method is applied to the (2+1)-dimensional nonisospectral Kadomtsev–Petviashvili equation with two Painlevé expansion branches to determine auto-Bäcklund transformation, Lax pairs and Darboux transformation. Based on the two obtained Lax pairs, the binary Darboux...
Anna Gierzkiewicz, Zdzisław A. Golda
Pages: 494 - 506
The Szekeres system is a four-dimensional system of ﬁrst-order ordinary differential equations with nonlinear but polynomial (quadratic) right-hand side. It can be derived as a special case of the Einstein equations, related to inhomogeneous and nonsymmetrical evolving spacetime. The paper shows how...
Pages: 494 - 498
We prove that a solution to the gravity water wave problem with constant vorticity, whose wave profile as well as its horizontal velocity component at the free surface are symmetric at any instant of time, is given by a traveling wave. The proof is based on maximum principles and structural properties...
Alexander V. Bobylev, Sergey V. Meleshko
Pages: 494 - 508
In this paper group properties of the so-called Generalized Burnett equations are studied. In contrast to the classical Burnett equations these equations are well-posed and therefore can be used in applications. We consider the one-dimensional version of the generalized Burnett equations for Maxwell...
Pages: 499 - 507
We consider the direct/inverse spectral problem for the periodic Camassa-Holm eqution. In fact, we survey the direct/inverse spectral problem for the periodic weighted operator Ly = m-1 (-y +1 4 y) acting in the space L2 (R, m(x)dx), where m = uxx-u > 0 is a 1-periodic positive function and u is the...
Pages: 499 - 506
The problem of three bodies which attract each other with forces proportional to the cube of the inverse of their distance and move on a line was reduced to one quadrature by Jacobi . Here we show that the equations of motions admit a five-dimensional Lie symmetry algebra and can be reduced to a...
Pages: 495 - 515
We identify a new class of algebraic relations satisfied by the zeros of orthogonal polynomials that are eigenfunctions of linear differential operators of order higher than two, known as Krall polynomials. Given an orthogonal polynomial family
, we relate the zeros of the polynomial...
Pages: 495 - 513
This paper is devoted to the negative flows of the derivative nonlinear Schrödinger hierarchy (DNLSH). The main result of this work is the functional representation of the extended DNLSH, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed...
Pages: 497 - 508
We exhibit some families of Riccati differential equations in the complex domain having elliptic coefficients and study the problem of understanding the cases where there are no multivalued solutions. We give criteria ensuring that all the solutions to these equations are meromorphic functions defined...
Pages: 499 - 506
In this paper we describe an exact, and explicit, three-dimensional nonlinear solution for geophysical internal ocean waves in the Equatorial region which incorporates a transverse-Equatorial meridional current.
Yu.A. Markov, M.A. Markova
Pages: 504 - 515
Stationary kinetic equations for a quark plasma (QP) in the Abelian dominance approximation are reduced to the nonlinear system of A2-periodic Toda chains (with elliptic operator). Using solutions of this system, which are found with the help of the first integrals and Hirota's method, such characteristics...
R. Sahadevan, S. Balakrishnan
Pages: 501 - 518
We report a new three and four coupled nonlinear partial differential-difference equations each admits Lax representation, possess infinitely many generalized (nonpoint) symmetries, conserved quantities and a recursion operator. Hence they are completely integrable both in the sense of Lax and Liouville.
Pages: 507 - 515
Considering the kinematics of the moving frame associated with a constant mean cuvature surface immersed in S3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S3 . The application of...
Satoru Odake, Ryu Sasaki
Pages: 507 - 521
Shape invariance is an important ingredient of many exactly solvable quantum mchanics. Several examples of shape invariant "discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of descriing the equilibrium positions of Ruijsenaars-Schneider type...
Pages: 508 - 520
We show that the smooth traveling waves of the Camassa-Holm equation naturally correspond to traveling waves of the Korteweg-de Vries equation.
Boris A. Kupershmidt
Pages: 508 - 517
Long-wave equations for an incompressible inviscid free-surface fluid in N + 1 dimesions are derived and shown to be Hamiltonian and liftable into the space of moments.
C. G. Böhmer, T. Harko
Pages: 503 - 516
In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Δu+un = 0 with u(0) = 1 and u′(0) = 0 on the positive real line, called the Emden–Fowler or Lane–Emden equation. This equation is of great importance in Newtonian astrophysics and the constant n is called the polytropic...
Jaume Llibre, Clàudia Valls
Pages: 505 - 516
We provide the complete classification of all global analytic first integrals of the simplified multistrain/two-stream model for tuberculosis and dengue fever that can be written as
with β1, β2, b, γ1, γ2, ν ∈ ℝ.
Pages: 511 - 531
We apply the Darboux theory of integrability to polynomial ODE's of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3dimensional LotkaVolterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases...
G. Gubbiotti, C. Scimiterna, D. Levi
Pages: 507 - 543
We discuss the non–autonomous nonlinear partial difference equations belonging to Boll classiﬁcation of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its Bäcklund transformations and Lax pairs. By...
Pages: 507 - 515
We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation...
Hongmin Li, Yuqi Li, Yong Chen
Pages: 509 - 520
In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure.
Runliang Lin, Robert Conte
Pages: 509 - 514
We provide a Lax pair for the surfaces of Voss and Guichard, and we show that such particular surfaces considered by Gambier are characterized by a third Painlevé function.
Jaume Llibre, Y. Paulina Martínez, Claudia Valls
Pages: 509 - 519
In this work we consider the Lotka–Volterra system in ℝ3
x˙=−x(x−y−z), y˙=−y(−x+y−z), z˙=−z(−x−y+z),
introduced recently in , and studied also in  and . In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they...
Francesco Calogero, Farrin Payandeh
Pages: 509 - 519
In this paper we identify certain peculiar systems of 2 discrete-time evolution equations,
which are algebraically solvable. Here ℓ is the “discrete-time” independent variable taking integer values (ℓ = 0, 1, 2,...), xn ≡ xn(ℓ) are 2 dependent variables, and x˜n≡xn(ℓ+1) are...
Pages: 516 - 524
Representations of the q-deformed Euclidean algebra Uq(iso3), which at q 1 gives the universal enveloping algebra U(iso3) of the Lie algebra iso3 of the Euclidean Lie group ISO(3), are studied. Explicit formulas for operators of irreducible -representations defined by two parameters R and s 1 2 Z are...
Vladimir P. Burskii
Pages: 516 - 522
In this paper we want to characterize nonlinear differential equations that describe processes allowing a localization operation in each subdomain of domain in which we consider the process. We formulate this localization condition by means of visual reresentations and give this operation a mathematical...
Min Ho Lee
Pages: 517 - 529
Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of 1, . . . , n with i = d/dxi for 1 i n. As in the single variable case, Lax equations can be constructed using such pseudodifferential operators, whose solutions can be provided by Baker functions. We...
Pages: 518 - 529
In this article we use thve Fokas transform method to analyze boundary value prolems for the sine-Gordon equation posed on a finite interval. The representation of the solution of this problem has already been derived using this transform method. We interchange the role of the independent variables to...
Pages: 518 - 533
The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamitonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure,...
Xin Huang, Boling Guo, Liming Ling
Pages: 514 - 528
Firstly, we establish the relation between the loop group method and gauge transformation method for 3×3 spectral problem. Some novel solutions of long wave-short wave model are obtained by Darboux transformation method. Besides, we give the analysis and classification of solution in detail.
Pages: 515 - 517
Certain nonlinearly-coupled systems of N discrete-time evolution equations are identified, which can be solved by algebraic operations; and some remarkable Diophantine findings are thereby obtained. These results might be useful to test the accuracy of numerical routines yielding the N roots of polynomials...
Pages: 521 - 533
We survey recent results on well-posedness, blow-up phenomena, lifespan and global existence for the Camassa-Holm equation. Results on weak solutions are also consiered.
Xiu-Bin Wang, Shou-Fu Tian, Chun-Yan Qin, Tian-Tian Zhang
Pages: 516 - 530
Under investigation in this work is the time-fractional generalized KdV-type equation, which occurs in different contexts in mathematical physics. Lie group analysis method is presented to explicitly study its vector fields and symmetry reductions. Furthermore, two straightforward methods are employed...
Calin Iulian Martin
Pages: 516 - 522
This paper is devoted to the subsurface current dynamics in equatorial regions, where the hallmark of a strong stratification is a sharp interface (thermocline), separating two layers of different density, and whose depth is dependent upon the strength of the winds above the ocean's surface. We...
Pages: 522 - 534
In this review we explain interrelations between the Elliptic Calogero-Moser model, the integrable Elliptic Euler-Arnold top, monodromy preserving equations and the Knizhnik-Zamolodchikov-Bernard equation on a torus.
R. Sahadevan, L. Nalinidevi
Pages: 517 - 538
It is shown that the deformed Nonlinear Schrödinger (NLS), Hirota and AKNS equations with (1 + 1) dimension admit infinitely many generalized (nonpoint) symmetries and polynomial conserved quantities, master symmetries and recursion operator ensuring their complete integrability. Also shown that each...
B. Agrebaoui, N. Ben Fraj, S. Omri
Pages: 523 - 534
We investigate the first cohomology space associated with the embedding of the Lie superalgebra K(2) of contact vector fields on the (1,2)-dimensional supercircle S1|2 in the Lie superalgebra SDO(S1|2 ) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we show...
Yanyan Ge, Kelei Tian, Xiaoming Zhu, Dafeng Zuo
Pages: 518 - 527
In this paper, we will construct free-field realizations of the
algebra associated to an
-valued differential operator
is a Frobenius algebra with the unit In.
M. Bruschi, F. Calogero, F. Leyvraz, M. Sommacal
Pages: 519 - 540
Recently we highlighted the remarkable nature of an explicitly invertible transformation, we reported some generalizations of it and examples of its expediency in several mathematical contexts: algebraic and Diophantine equations, dynamical systems (with continuous and discrete time), nonlinear PDEs,...
Shulin Lyu, James Griffin, Yang Chen
Pages: 520 - 535
The ‘restoration method’ is a novel method we recently introduced for systematically deriving discrete Painlevé equations. In this method we start from a given Painlevé equation, typically with E8(1) symmetry, obtain its autonomous limit and construct all possible QRT-canonical forms of mappings that...
Sasanka Ghosh, Debojit Sarma
Pages: 526 - 538
The N = 2 super-KP equation associated with nonstandard flows is bilinearized using the Hirota method and soliton solutions are obtained. The bilinearization has been done for component fields and its KdV limit is discussed by comparing the soliton solutions obtained by this procedure with those found...
Diego Catalano Ferraioli, Paola Morando
Pages: 521 - 532
Solvable structures are particularly useful in the integration by quadratures of ordinary differential equations. Nevertheless, for a given equation, it is not always possible to compute a solvable structure. In practice, the simplest solvable structures are those adapted to an already known system of...
Marianna Euler, Norbert Euler
Pages: 521 - 528
This is a follow-up paper to the results published in Studies in Applied Mathematics 143, 139–156 (2019), where we reported a classification of 3rd- and 5th-order semi-linear symmetry-integrable evolution equations that are invariant under the Möbius transformation, which includes a list of fully nonlinear...
Pages: 527 - 533
In this paper we use the Painlev Ìe analysis and study a special case of a water wave equation of the KdV type. More specifically, we use the Pickering algorithm  and obtain a new kind of solutions, which constitute of both algebraic and trigonometric (or hyperbolic) functions.
Pages: 523 - 530
In this paper we present a dynamical study of the exact nonlinear Pollard wave solution to the geophysical water-wave problem in the f-plane approximation. We deduce an exact dispersion relation and we discuss some properties of this solution.
Wei Feng, Song-Lin Zhao, Da-Jun Zhang
Pages: 524 - 538
In this paper several kinds of exact solutions to lattice Boussinesq-type equations are constructed by means of generalized Cauchy matrix approach, including soliton solutions and mixed solutions. The introduction of the general condition equation set yields that all solutions contain two kinds of plane-wave...
Pages: 530 - 550
It is shown how the bilinear differential equations satisfied by Fredholm determinants of integral operators appearing as spectral distribution functions for random matrices may be deduced from the associated systems of nonautonomous Hamiltonian equations satisfied by auxiliary canonical phase space...
Wojtek J. Zakrzewski
Pages: 530 - 538
We consider some lattices and look at discrete Laplacians on these lattices. In partiular we look at solutions of the equation (1) = (2)Z, where (1) and (2) denote two such Laplacians on the same lattice. We show that, in one dimension, when (i), i = 1, 2, denote (1) = (i + 1) + (i - 1) - 2(i) and (2)Z...
George W. Bluman, Omar Mrani-Zentar, Deshin Finlay
Pages: 528 - 557
It is shown explicitly how one can obtain elements of Lie groups as compositions of products of other elements based on the commutator properties of associated Lie algebras. Problems of this kind can arise naturally in control theory. Suppose an apparatus has mechanisms for moving in a limited number...
Alberto Molgado, Adan Rodríguez
Pages: 534 - 547
In this work we investigate a formal mapping between the dynamical properties of the unidimensional relativistic oscillator and the asymmetrical rigid top at a clas- sical level. We study the relativistic oscillator within Yamaleevâ€™s interpretation of Nambu mechanics. Such interpretation is based on...
Pages: 534 - 548
The goal of this survey article is to explain the up-to-date state of the theory of Lp - Lq decay estimates for wave equations with time-dependent coefficients. We explain the influence of oscillations in the coefficients by using a precise classification. Moreover, we will see how mass and dissipation...
Yuri B. Suris
Pages: 534 - 560
A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra e(n) = so(n) Rn . We give a Lagrangian derivation of the corresponding equations of motion, and introduce discrete time analogs of two integrable...
Jipeng Cheng, Maohua Li, Jingsong He
Pages: 529 - 538
With the help of the squared eigenfunction potential, the action of the Virasoro symmetry on the tau function of the constrained discrete KP hierarchy is derived.
Vincent Chalifour, Alfred Michel Grundland
Pages: 529 - 549
This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces approach defined by the Enneper-Weierstrass formula for immersion and...