Journal of Nonlinear Mathematical Physics

Volume 22, Issue 2, February 2015
Research Article

1. No periodic orbits for the type A Bianchi's systems

Claudio A. Buzzi, Jaume Llibre
Pages: 170 - 179
It is known that the 6 models of Bianchi class A have no periodic solutions. In this article we provide a new, direct, unified and easier proof of this result.
Research Article

2. Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach

Shou-Fu Tian, Tian-Tian Zhang, Pan-Li Ma, Xing-Yong Zhang
Pages: 180 - 193
By using the extended Harrison and Estabrook's differential forms approach, in this paper, we investigate the Lie symmetries of the continuous and discrete dispersive long waves system, respectively. Based on this method, two closed ideals written in terms of a set of differential forms are constructed...
Research Article

3. On generalized Lax equation of the Lax triple of KP Hierarchy

Xiao-Li Wang, Lu Yu, Yan-Xin Yang, Min-Ru Chen
Pages: 194 - 203
In terms of the operator Nambu 3-bracket and the Lax pair (L, Bn) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, Bn, Bm). The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized...
Research Article

4. On a supersymmetric nonlinear integrable equation in (2+1) dimensions

Zhigang Yin, Lu Yu, Minli Li
Pages: 204 - 209
A supersymmetric integrable equation in (2+1) dimensions is constructed by means of the approach of the homogenous space of the super Lie algebra, where the super Lie algebra osp(3/2) is considered. For this (2+1) dimensional integrable equation, we also derive its Bäcklund transformation.
Research Article

5. Integrability properties of some equations obtained by symmetry reductions

H. Baran, I.S. Krasil′shchik, O.I. Morozov, P. Vojčák
Pages: 210 - 232
In our recent paper [1], we gave a complete description of symmetry reduction of four Lax-integrable (i.e., possessing a zero-curvature representation with a non-removable parameter) 3-dimensional equations. Here we study the behavior of the integrability features of the initial equations under the reduction...
Research Article

6. Inverse Scattering Transform for the Discrete Focusing Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions

Cornelis van der Mee
Pages: 233 - 264
In this article we develop the direct and inverse scattering theory of the Ablowitz-Ladik system with potentials having limits of equal positive modulus at infinity. In particular, we introduce fundamental eigensolutions, Jost solutions, and scattering coefficients, and study their properties.We also...
Research Article

7. Symmetries of some classes of dynamical systems

Cristian Lăzureanu, Tudor Bînzar
Pages: 265 - 274
In this paper a three-dimensional system with five parameters is considered. For some particular values of these parameters, one finds known dynamical systems. The purpose of this work is to study some symmetries of the considered system, such as Lie-point symmetries, conformal symmetries, master symmetries...
Research Article

8. Speed selection for coupled wave equations

Mariano Cadoni, Giuseppe Gaeta
Pages: 275 - 297
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding (multi-component) travelling wave solutions under certain physical conditions....
Research Article

9. The Bilinear Integrability, N-soliton and Riemann-theta function solutions of B-type KdV Equation

Jianqin Mei, Lijuan Wu
Pages: 298 - 307
In this paper, the bilinear integrability for B-type KdV equation have been explored. According to the relation to tau function, we find the bilinear transformation and construct the bilinear form with an auxiliary variable of the B-type KdV equation. Based on the truncation form, the Bäcklund transformation...
Research Article

10. Some extensions on the soliton solutions for the Novikov equation with cubic nonlinearity

Chaohong Pan, Yating Yi
Pages: 308 - 320
In this paper, by using the bifurcation method of dynamical systems, we derive the traveling wave solutions of the nonlinear equation UUτyy − UyUτy + U2Uτ + 3Uy = 0. Based on the relationship of the solutions between the Novikov equation and the nonlinear equation, we present the parametric representations...