Zhang Jie-Fang

Chaos and Fractals in a (2+1)-Dimensional Soliton System

Considering that there are abundant coherent soliton excitations in high dimensions, we reveal a novel phenomenon that the localized excitations possess chaotic and fractal behaviour in some (2+1)-dimensional soliton systems. To clarify the interesting phenomenon, we take the generalized (2+1)-dimensional Nizhnik-Novikov-Vesselov system as a concrete example. A quite general variable separation solutions of this system is derived via a variable separation approach first, then some new excitations like chaos and fractals are derived by introducing some types of lower-dimensional chaotic and fractal patterns.

Symbolic Computation of Extended Jacobian Elliptic Function Algorithm for Nonlinear Differential-Different Equations

The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.

NEW EXACT SOLITARY WAVE SOLUTIONS OF THE KS EQUATION

Two methods are described for obtaining newexact solitary wave solutions of the KS equation.Because these two methods are essentially equivalent theresults obtained here are the same.

Variable Separation Solutions in （1＋1）-Dimensional and （3＋1）-Dimensional Systems via Entangled Mapping Approach

In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1+1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3+1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2+1)-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.

General Solution and Fractal Localized Structures for the (2+1)-Dimensional Generalized Ablowitz-Kaup-Newell-Segur System

Using the standard truncated Painleve expansions, we derive a quite general solution of the (2+1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system. Except for the usual localized solutions, such as dromions, lumps, ring soliton solutions, etc, some special localized excitations with fractal behaviour, i.e. the fractal dromion and fractal lump excitations, are obtained by some types of lower-dimensional fractal patterns.

Optical Solitary Waves in Fourth-Order Dispersive Nonlinear Schrödinger Equation with Self-steepening and Self-frequency Shift

By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitary wave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.

Variable separation solutions and new solitary wave structures to the (1+1)-dimensional Ito system

A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1+1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.

Bäcklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation

We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a B?cklund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.

Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation

This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.

Multiple Soliton-Like Solutions for (2 + 1)-Dimensional Dispersive Long-Wave Equations

By using a homogeneous balance method,multiple-solitonlike solutions of the (2 +1)-dimensional dispersive long-wave equation areconstructed. The method used here can be generalized toa wide class of nonlinear evolution equations.