Journal of Nonlinear Mathematical Physics

Volume 19, Issue 4, December 2012
Research Article

1. A New (γn, σk)-KP Hierarchy and Generalized Dressing Method

Yuqin Yao, Yehui Huang, Yunbo Zeng
Pages: 445 - 457
A new (γn, σk)-KP hierarchy (KPH) with two new time series γn and σk, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. Two reductions and constrained flows of (γn, σk)-KPH are studied. The dressing method is generalized to the (γn, σk)-KPH and...
Research Article

2. On the Application of a Generalized Version of the Dressing Method to the Integration of Variable Coefficient N-Coupled Nonlinear Schrödinger Equation

Ting Su, Huihui Dai, Xian Guo Geng
Pages: 458 - 476
N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are...
Research Article

3. On the Integrability of a Muthuswamy–Chua System

Jaume Llibre, Claudia Valls
Pages: 477 - 488
In this paper we study the integrability of the Muthuswamy–Chua system x'=y,y'=-x3+y2-yz22,z'=y-αz-yz. 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...
Research Article

4. Quasi-Periodic Solutions of the Relativistic Toda Hierarchy

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...
Research Article

5. Exact Solutions to Lattice Boussinesq-Type Equations

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...
Research Article

6. Octahedral Structure of the Hirota–Miwa Equation

Satoru Saito
Pages: 539 - 550
The Hirota–Miwa equation is studied from the view point of derived category.
Research Article

7. Landau Levels in a Two-Dimensional Noncommutative Space: Matrix and Quaternionic Vector Coherent States

Mahouton Norbert Hounkonnou, Isiaka Aremua
Pages: 551 - 579
The behavior of an electron in an external uniform electromagnetic background coupled to an harmonic potential, with noncommuting space coordinates, is considered in this work. The thermodynamics of the system is studied. Matrix vector coherent states (MVCS) as well as quaternionic vector coherent states...
Research Article

8. Group of Transformations with Respect to the Counterpart of Rapidity and Related Field Equations

Adán R. Rodríguez-Domínguez, Alejandro Martínez-González
Pages: 580 - 594
The Lorentz-group of transformations usually consists of linear transformations of the coordinates, keeping as invariant the norm of the four-vector in (Minkowski) space-time. Besides those linear transformations, one may construct different forms of nonlinear transformations of the coordinates keeping...
Research Article

9. Darboux Integrability of a Simplified Friedman–Robertson–Walker Hamiltonian System

Jaume Llibre, Clàudia Valls
Pages: 607 - 617
We characterize the Darboux first integrals of a simplified Friedman–Robertson–Walker Hamiltonian system depending on one parameter.