Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy

A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS) hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv.

New Types of Interactions between Solitons of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation

By means of the extended homogeneous balance method and the variable separation approach, more general variable separation solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation are obtained. Based on the variable separation solution and by selecting appropriate functions, new types of interactions between the multi-valued and the single-valued solitons, such as compactonlike semi-foldon and compacton, peakon-like semi-foldon and peakon, and bell-like semi-foldon and dromion, are investigated. Meanwhile, we also discuss the phase shift of these interactions. - PACS: 02.30.Jr, 02.30.Ik

Exact Localized and Periodic Solutions of the Ablowitz-Ladik Discrete Nonlinear Schrödinger System

We have studied, analytically, the Ablowitz-Ladik discrete nonlinear Schr¨odinger system. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobian functions, bright and dark soliton solutions, and quasi-periodic solutions. We have also found the range of parameters where each exact solution exists. - PACS: 02.30.Jr, 05.45.Yv, 42.65.Tg, 02.30.Gp.

Non-polynomial Fourth Order Equations which Pass the Painlevé Test

The singular point analysis of fourth order ordinary differential equations in the non-polynomial class are presented. Some new fourth order ordinary differential equations which pass the Painlevé test as well as the known ones are found. -PACS: 02.30.Hq, 02.30.Ik, 02.30.Gp

Jacobi Elliptic Function Solutions of Three Coupled Nonlinear Physical Equations

The Jacobi elliptic function solutions of coupled nonlinear partial differential equations, including the coupled modified KdV (mKdV) equations, long-short-wave interaction system and the Davey- Stewartson (DS) equations, are obtained by using the mixed dn-sn method. The solutions obtained in this paper include the single and the combined Jacobi elliptic function solutions. In the limiting case, the solitary wave solutions of the systems are also given. - PACS: 02.30.Jr; 03.40.Kf; 03.65.Fd

Travelling And Periodic Wave Solutions Of Some Nonlinear Wave Equations

We present the mixed dn-sn method for finding periodic wave solutions of some nonlinear wave equations. Introducing an appropriate transformation, we extend this method to a special type of nonlinear equations and construct their solutions, which are not expressible as polynomials in the Jacobi elliptic functions. The obtained solutions include the well known kink-type and bell-type solutions as a limiting cases. Also, some new travelling wave solutions are found. - PACS: 02.30.Jr; 03.40.Kf

Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable equation. We use the Weierstrass elliptic equation as building block to find a number of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fourth order with special solutionsexpressed via theWeierstrass function are given. - PACS: 02.30.Hq (Ordinary differential equations)

A General ANNV Family with a Common Special Kac-Moody-Virasoro Symmetry Algebra

A general asymmetric Nizhnik-Novikov-Veselov (ANNV) family with an arbitrary function of high order group invariants is proposed. It is proved that the general ANNV family possesses a common infinite dimensional Kac-Moody-Virasoro symmetry algebra. The Kac-Moody-Virasoro group invariant solutions and the Kac-Moody group invariant solutions of the ANNV family are also studied.- PACS: 02.30.Jr, 02.30.Ik, 05.45.Yv.

Elliptic Function Solutions of (2+1)-dimensional Longwave – Shortwave Resonance Interaction Equation via a sinh-Gordon Expansion Method

With the aid of symbolic computation, the sinh-Gordon equation expansion method is extended to seek Jacobi elliptic function solutions of (2+1)-dimensional long wave-short wave resonance interaction equation, which describe the long and short waves propagation at an angle to each other in a two-layer fluid. As a result, new Jacobi elliptic function solutions are obtained. When the modulus m of Jacobi elliptic functions approaches 1, we also deduce the singular oliton solutions; while when the modulus m→0, we get the trigonometric function solutions. - PACS: 02.30.Jr, 03.40.Kf