Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave－short-wave resonant interaction

A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave－short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.     

Soliton excitations and chaotic patterns for the (2+1)-dimensional Boiti-Leon-Pempinelli system

By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated.     

Chaotic behaviors of the （2＋1）-dimensional generalized Breor-Kaup system

With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the(2+1)-dimensional generalized Breor-Kaup(GBK) system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.     

Instantaneous solitons and fractal solitons for a (2+1)-dimensional nonlinear system

By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek--Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.     

Chaotic solutions of (2+1)-dimensional Broek Kaup equation with variable coefficients

In this paper,an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup equation with variable coefficients (VCBK). Based on the derived solitary wave solution and using a known chaotic system,some novel chaotic solutions are investigated.     

New Exact Solutions and Interactions Between Two Solitary Waves for （3＋1）-Dimensional Jimbo-Miwa System

By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the （3＋1）-dimensional Jimbo-Miwa system is derived. Based on the derived solitary wave solution, we obtain some special localized excitations and study the interactions between two solitary waves of the system.     

Complex solutions and novel complex wave localized excitations for the(2+1)-dimensional Boiti–Leon–Pempinelli system

With the help of the symbolic computation system Maple, the Riccati equation mapping approach and a linear variable separation approach, a new family of complex solutions for the （2＋ 1）-dimensional Boiti-Leon-Pempinelli system （BLP） is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations are obtained.     

Folded localized excitations in the （2＋1）-dimensional modified dispersive water-wave system

By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.     

New Family of Exact Solutions and Chaotic Soltions of Generalized Breor-Kaup System in （2＋1）-Dimensions via an Extended Mapping Approach

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized （2＋1）-dimensional Broer-Kaup system （GBK） system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the （2＋1）-dimensional GBK system.     

Annihilation Solitons and Chaotic Solitons for the （2＋1）-Dimensional Breaking Soliton System

By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.     

(2+1)维色散长波方程的新精确解及其复合波激发

利用Riccati方程展开法和变量分离法,得到了(2+1)维色散长波方程的变量分离解.根据得到的孤波解,构造出该方程新颖的复合波局域结构,研究了复合波随时间的演化.     

(3+1)维Burgers系统的新精确解及其特殊孤子结构

将改进的Riccati方程映射法和变量分离法推广到(3+1)维Burgers系统,得到了该系统的新显式精确解.根据得到的孤波解,构造出Burgers系统的几种特殊孤子结构,例如柱状孤子、状孤子和内嵌孤子等,研究了孤子间的相互作用. 关键词： 改进的映射法 (3+1)维Burgers系统 孤子结构 相互作用     

Complex Wave Excitations in Generalized Broer-Kaup System

Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.     

(1+1)维耦合Ito系统的单值和多值局域激发模式

在(1 1)维非线性动力学系统,人们发现不同的局域激发模式分别存在于不同的非线性系统.可是最近的若干研究表明,在高维非线性动力学系统中,如果选取适当的边值条件或初始条件时,人们可以同时找到若干不同的局域激发模式,如:紧致子、峰孤子、呼吸子和折叠子等.本文的主要目的是寻找(1 1)维非线性耦合Ito系统中的不同的局域激发模式.首先,基于一个特殊的Painlev-éBacklund变换和线性变量分离方法,求得了该系统具有若干任意函数的变量分离严格解.然后,根据得到的变量分离严格解,通过选择严格解中的任意函数,引入恰当的单值分段连续函数和多值局域函数,成功找到了耦合Ito系统若干有实际物理意义的单值和多值局域激发模式,如:峰孤子,紧致子和多圈孤子等.     

New Families of Rational Form Variable Separation Solutions to （2＋1）-Dimensional Dispersive Long Wave Equations

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.