Journal of Nonlinear Mathematical Physics

Volume 14, Issue 1, February 2007
Research Article

1. Particle trajectories in linear periodic capillary and capillary-gravity deep-water waves

David Henry
Pages: 1 - 7
We show that within the framework of linear theory the particle paths in a periodic gravity-capillary or pure capillary deep-water wave are not closed.
Research Article

2. An invariant p-adic q-integral associated with q-Euler numbers and polynomials

Ismail Naci Cangül, Veli Kurt, Yilmaz Simsek, Hong Kyung Pak, Seog-Hoon Rim
Pages: 8 - 14
The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf. [1, 3, 6, 12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using...
Research Article

3. q-Euler numbers and polynomials associated with p-adic q-integrals

Taekyun Kim
Pages: 15 - 27
The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple...
Research Article

4. The Initial-Boundary Value Poblem for the Korteweg-de Vries Equation on the Positive Quarter-Plane

Pham Loi Vu
Pages: 28 - 43
The paper deals with a problem of developing an inverse-scattering transform for solving the initial-boundary value problem (IBVP) for the Korteweg-de Vries equation on the positive quarter-plane: pt - 6ppx + pxxx = 0, x 0, t 0, (a) with the given initial and boundary conditions: p(x, 0) = p(x), p(x)...
Research Article

5. New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials

Yilmaz Simsek, Veli Kurt, Daeyeoul Kim
Pages: 44 - 56
In this paper, by using q-Volkenborn integral[10], the first author[25] constructed new generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. We define higher-order twisted (h, q)-Bernoulli polynomials and numbers. Using these numbers and polynomials, we obtain new approach...
Research Article

6. Solitons in Yakushevich-like models of DNA dynamics with improved intrapair potential

Giuseppe Gaeta
Pages: 57 - 81
The Yakushevich model provides a very simple pictures of DNA torsion dynamics, yet yields remarkably correct predictions on certain physical characteristics of the dynamics. In the standard Yakushevich model, the interaction between bases of a pair is modelled by a harmonic potential, which becomes anharmonic...
Research Article

7. A note on the relationship between rational and trigonometric solutions of the WDVV equations

Andrew Riley, Ian A.B. Strachan
Pages: 82 - 94
Legendre transformations provide a natural symmetry on the space of solutions to the WDVV equations, and more specifically, between different Frobenius manifolds. In this paper a twisted Legendre transformation is constructed between solutions which define the corresponding dual Frobenius manifolds....
Research Article

8. A geometric interpretation of the complex tensor Riccati equation for Gaussian beams

M.F. Dahl
Pages: 95 - 111
We study the complex Riccati tensor equation DcG + GCG - R = 0 on a geodesic c on a Riemannian 3-manifold. This non-linear equation appears in the study of Gaussian beams. Gaussian beams are asymptotic solutions to hyperbolic equations that at each time instant are concentrated around one point in space....
Research Article

9. On sl(2)-relative cohomology of the Lie algebra of vector fields and differential operators

Sofiane Bouarroudj
Pages: 112 - 127
Let Vect(R) be the Lie algebra of smooth vector fields on R. The space of symbols Pol(T R) admits a non-trivial deformation (given by differential operators on weighted densities) as a Vect(R)-module that becomes trivial once the action is restricted to sl(2) Vect(R). The deformations of Pol(T R), which...
Research Article

10. Solitons in a double pendulums chain model, and DNA roto-torsional dynamics

Mariano Cadoni, Roberto De Leo, Giuseppe Gaeta
Pages: 128 - 146
It was first suggested by Englander et al to model the nonlinear dynamics of DNA relevant to the transcription process in terms of a chain of coupled pendulums. In a related paper [4] we argued for the advantages of an extension of this approach based on considering a chain of double pendulums with certain...
Research Article

11. On application of Liouville type equations to constructing Bäcklund transformations

Dmitry Demskoi
Pages: 147 - 156
It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transformations are found. In particular we obtained the Bäcklund transformations for a pair of three-component analogs of the dispersive...