Journal of Nonlinear Mathematical Physics

Latest Articles

Fuzzy Relational Fixed Point Clustering

Roelof K. Brouwer
Volume 2, Issue 1, March 2009, Pages 69-82
The proposed relational fuzzy clustering method, called FRFP ( fuzzy relational fixed point), is based on determining a fixed point of a function of the desired membership matrix. The ethod is compared to other relational clustering methods. Simulations show the method to be very effective and less computationally...

Novel Robust Stability Criteria for Uncertain Stochastic Neural Networks with Time-Varying Delay

Yunrui Guo, Yonggang Chen, Wenlin Li
Volume 2, Issue 1, March 2009, Pages 1-9
This paper considers the robust stability analysis problem for a class of uncertain stochastic neural net- works with time-varying delay. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the stochastic derivative of Lyapunov functionals,...

Feature Weighting and Retrieval Methods for Dynamic Texture Motion Features

Ashfaqur Rahman, Manzur Murshed
Volume 2, Issue 1, March 2009, Pages 27-38
Feature weighing methods are commonly used to find the relative significance among a set of features that are effectively used by the retrieval methods to search image sequences efficiently from large databases. As evidenced in the current literature, dynamic textures (image sequences with regular motion...

Doubly periodic waves of a discrete nonlinear Schrodinger system with saturable nonlinearity

Robert Conte, K. W. Chow
Volume 15, Issue 4, December 2008, Pages 398-409
A system of two discrete nonlinear Schr¨odinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-product, several new solutions of the elliptic type are provided for NLS-type discrete and continuous...

Asymptotically isochronous systems

Francesco Calogero, David Gomez-Ullate
Volume 15, Issue 4, December 2008, Pages 410-426
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the same fixed period. We focus on two such mechanisms, emphasizing...

Solutions of some second order ODEs by the extended Prelle-Singer method and symmetries

A. Ghose Choudhury, Partha Guha, Barun Khanra
Volume 15, Issue 4, December 2008, Pages 365-382
In this paper we compute first integrals of nonlinear ordinary differential equations using the extended Prelle-Singer method, as formulated by Chandrasekar et al in J. Math. Phys. 47 (2), 023508, (2006). We find a new first integral for the Painlev´e-Gambier XXII equation. We also derive the first integrals...

Contiguity relations for discrete and ultradiscrete Painleve equations

A Ramani, B. Grammaticos, R. Willox
Volume 15, Issue 4, December 2008, Pages 353-364
We show that the solutions of ultradiscrete Painleve equations satisfy contiguity relations just as their continuous and discrete counterparts. Our starting point are the relations for q-discrete Painleve equations which we then proceed to ultradiscretise. In this paper we obtain results for the one-parameter...

Symmetry analysis for Whitham-Broer-Kaup equations

Zhiyong Zhang, Xuelin Yong, Yufu Chen
Volume 15, Issue 4, December 2008, Pages 383-397
We investigate a further group analysis of Whitham-Broer-Kaup(for short WBK) equations. An optimal system of one-dimensional subalgebras is derived and used to construct reduced equations and similarity solutions. Moreover, a special case of WBK equations is linearized and some new solutions are obtained....

Polynomial integrals for third- and fourth-order ordinary difference equations

R. Sahadevan, C. Uma Maheswari
Volume 15, Issue 3, November 2008, Pages 299-315
A direct method to construct polynomial integrals for third order ordinary difference equation (OE) w(n + 3) = F(w(n),w(n + 1),w(n + 2)) and fourth order OE w(n+4) = F(w(n),w(n+1),w(n+2),w(n+3)) is presented. The effectiveness of the method to construct more than one polynomial integral for N-th order...

A new extended q-deformed KP hierarchy

Runliang Lin, Xiaojun Liu, Yunbo Zeng
Volume 15, Issue 3, November 2008, Pages 333-347
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy...

On an inverse scattering algorithm for the Camassa-Holm equation

Octavian G. Mustafa, Donal O'Regan
Volume 15, Issue 3, November 2008, Pages 283-290
We present a clarification of a recent inverse scattering algorithm developed for the Camassa-Holm equation.

Conservation Laws and Non-Lie Symmetries for Linear PDEs

Anthony C. L. Ashton
Volume 15, Issue 3, November 2008, Pages 316-332
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including those of the non-Lie type. An explicit example is made of the...

A special class of holomorphic mappings and the Faddeev-Hopf model

Radu Slobodeanu
Volume 15, Issue 3, November 2008, Pages 270-282
Pseudo horizontally weakly conformal maps [16] extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find critical points for the (generalized) Faddeev-Hopf model [28] in this larger class.

Fordy-Kulish model and spinor Bose-Einstein condensate

V. A. Atanasov, V. S. Gerdjikov, G G Grahovski, N. A. Kostov
Volume 15, Issue 3, November 2008, Pages 291-298
A three-component nonlinear Schrodinger-type model which describes spinor Bose-Einstein condensate (BEC) is considered. This model is integrable by the inverse scattering method and using Zakharov-Shabat dressing method we obtain three types of soliton solutions. The multi-component nonlinear Schr¨odinger...

A Hidden Group Structure for the Integrals of the Benney System

Boris A. Kupershmidt
Volume 15, Issue 3, November 2008, Pages 348-352
The integrals of the Benney system are shown to possess a group structure. The KP hierarchy breaks the group law down.

Partially Solvable Spin Chains and QES Spin Models

A. Enisco, F. Finkel, A. Gonzalez-Lopez, M.A. Rodriguez
Volume 15, Issue supplement 3, October 2008, Pages 155-165
In this paper we prove an extension of the usual freezing trick argument which can be applied to a number of quasi-exactly solvable spin models of Calogero­Sutherland type. In order to illustrate the application of this method we analyze a partially solvable spin chain presenting near-neighbors interactions...

On the Origin of Fractional Shapiro Steps in Systems of Josephson Junctions with Few Degrees of Freedom

A Valizadeh, M. R. Kolahchi, J. P. Straley
Volume 15, Issue supplement 3, October 2008, Pages 407-416
We investigate the origin of fractional Shapiro steps in arrays consisting of a few overdamped Josephson junctions. We show that when the symmetry reduces the equations to that of a single junction equation, only integer steps appear. Otherwise, fractional steps will appear when the evolution equations...

Existence of Dark Soliton Solutions of the Cubic Nonlinear Schrödinger Equation with Periodic Inhomogeneous Nonlinearity

Juan Belmonte-Beitia, Pedro J Torres
Volume 15, Issue supplement 3, October 2008, Pages 65-72
In this paper, we give a proof of the existence of stationary dark soliton solutions of the cubic nonlinear Schrödinger equation with periodic inhomogeneous nonlinearity, together with an analytical example of a dark soliton.

Corrugated Surfaces with Slow Modulation and Quasiclassical Weierstrass Representation

B. G. Konopelchenko
Volume 15, Issue supplement 3, October 2008, Pages 227-236
Quasiclassical generalized Weierstrass representation for highly corrugated surfaces in R3 with slow modulation is proposed. Integrable deformations of such surfaces are described by the dispersionless modified Veselov-Novikov hierarchy.

Integrating Factors and - Symmetries

C. Muriel, J. L. Romero
Volume 15, Issue supplement 3, October 2008, Pages 300-309
We investigate the relationship between integrating factors and -symmetries for ordinary differential equations of arbitrary order. Some results on the existence of -symmetries are used to prove an independent existence theorem for integrating factors. A new method to calculate integrating factors and...

A Common Integrable Structure in the Hermitian Matrix Model and Hele-Shaw Flows

L. Martinez Alonso, E. Medina
Volume 15, Issue supplement 3, October 2008, Pages 277-287
It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in Hele-Shaw flows.

Lift of Invariant to Non-Invariant Solutions of Complex Monge-Ampère Equations

M. B. Sheftel, A. A. Malykh
Volume 15, Issue supplement 3, October 2008, Pages 385-395
We show how partner symmetries of the elliptic and hyperbolic complex Monge-Ampère equations (CMA and HCMA) provide a lift of non-invariant solutions of three- and twodimensional reduced equations, i.e., a lift of invariant solutions of the original CMA and HCMA equations, to non-invariant solutions...

Evolution of Kink Network in Inhomogenous Systems

T Dobrowolski, P. Tatrocki
Volume 15, Issue supplement 3, October 2008, Pages 144-154
The purpose of this report is to show the influence of imperfections on creation and evolution of a kink network. Our main finding is a mechanism for reduction of the kinetic energy of kinks which works in both the overdamped and underdamped regimes. This mechanism reduces mobility of kinks and therefore...

Changing Solitons in Classical & Quantum Integrable Defect and Variable Mass Sine-Gordon Model

Anjan Kundu
Volume 15, Issue supplement 3, October 2008, Pages 237-250
Sine-Gordon (SG) models with position dependent mass or with isolated defects appear in many physical situations, ranging from fluxon or semi-fluxon in nonuniform Josephson junction to spin-waves in quantum spin chain with variable coupling or DNA solitons in the active promoter region. However such...

Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation

Hans Lundmark, Jacek Szmigielski
Volume 15, Issue supplement 3, October 2008, Pages 264-276
We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We derive and solve ODEs governing the soliton dynamics, first for...