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.     

Complex wave excitations general （2＋1）-dimensional and chaotic patterns for a Korteweg-de Vries system

Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV     

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.     

Variable Separation Approach to Solve (2 + 1)-Dimensional Generalized Burgers System:Solitary Wave and Jacobi Periodic Wave Excitations

By means of the standard truncated Painlev\'{e} expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations --- compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.     

Localized Coherent Structures with Chaotic and Fractal Behaviors in a （2＋l）－Dimensional Modified Dispersive Water－Wave System

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 l)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable located coherent soliton excitations like dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractal behaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.     

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.     

Localized Coherent Structures with Chaotic and Fractal Behaviors in a(2+1)-Dimensional Modified Dispersive Water-Wave System

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1 )-dimensionalphysical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 1)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable localized coherent soliton excitationslike dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractalbehaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.     

Periodic Semifolded Solitary Waves for （2＋1）-Dimensional Variable Coefficient Broer-Kaup System

Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the （2＆1 ）-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.     

(3+1)维Burgers系统的瞬内嵌孤子和瞬锥形孤子

利用投射方程法和变量分离法,得到了(3+1)维Burgers系统的变量分离解(包括孤波解、周期波解和有理函数解).根据孤波解和有理函数解,构造出Burgers系统新颖的局域结构,例如瞬内嵌孤子和瞬锥形孤子.     

Fusion and fission solitons for the (2+1)-dimensional generalized Breor-Kaup system

With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (2+1)-dimensional generalized Breor-Kaup (GBK) system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons.     

Fractal Structures and Chaotic Behaviors in a （2＋1）-Dimensional Nonlinear System

With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.     

扩展的(2+1)维浅水波方程的尖峰孤子解及其相互作用

利用改进的 Riccati方程映射法和变量分离法, 得到了扩展的(2+1)维浅水波方程的变量分离解(包括孤波解, 周期波解和有理函数解). 根据得到的孤波解, 构造出了方程的几种不同形状的尖峰孤子结构, 研究了孤子的相互作用.     

(2+1)维非对称 Nizhnik-Novikov-Veselov系统的新映射解及其局域结构

映射法是一种非常经典、有效和成熟的求解非线性演化方程的方法，其最大的特点是可以有多种不同形式的设解，使得最终求得的解丰富多彩. 利用改进的 Riccati 方程映射法和变量分离法，得到了(2+1)维非对称 Nizhnik-Novikov-Veselov 系统的新显式精确解.根据得到的孤波解，构造出该系统的峰孤子和分形孤子等局域结构，研究了两个孤立波的“追碰”现象. 关键词： 改进的映射法 (2+1)维非对称 Nizhnik-Novikov-Veselov 系统 局域结构 “追碰”现象     

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.     

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.     

New exact solutions of (3+1)-dimensional Jimbo-Miwa system

By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we obtain some special localized excitations and study the interactions between two solitary waves of the system.     

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.     

New exact solutions of a （3＋1）-dimensional Jimbo-Miwa system

By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we obtain some special localized excitations and study the interactions between two solitary waves of the system.     

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.