A Series of Variable Separation Solutions and New Soliton Structures of （2＋1）-Dimensional Korteweg-de Vries Equation

Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model （24）. Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.     

Study on (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation by Using Extended Mapping Approach

Extended mapping approach is introduced to solve (2 1)-dimensional Nizhnik-Novikov-Veselov equation.A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation,rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.     

The study of soliton fission and fusion in (2+1)-dimensional nonlinear system

By means of a variable separation approach and an extended homogeneous balance method, a general variable separation excitation of a (2+1)-dimensional nonlinear system is derived. Based on the derived solution with arbitrary functions, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system.     

(2+1)维非线性Burgers方程变量分离解和新型孤波结构

利用变量分离方法，获得了(2+1)维非线性Burgers方程的变量分离解.由于在Bcklund变换和变量分离步骤中引入了作为种子解的任意函数, 因而精确解中含有三个任意函数(其中一个为条件函数),适当地选择任意函数，可以获得多种形状的扭状孤波解、周期性孤子解和格子型孤波解. 关键词： 变量分离解 非线性波方程 （2+1）维     

Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation

A variable separation approach is proposed and successfully extended to the (1 1)-dimensional physics models. The new exact solution of (1 1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.     

(2+1)维非线性KdV方程的新孤子结构

通过选取另一类种子解，给出了(2+1)维非线性KdV方程的一类变量分离新解.适当地选择变量分离新解中的任意函数和条件函数，揭示了一类新型孤子结构，如周期性孤波结构、环状孤子结构、曲线型孤子结构等.可以发现(2+1)维非线性KdV方程存在的这类新型孤子结构，是无法通过以往文献中给出的通用变量分离表达式得到的，而且这类新型孤子结构对于实际自然现象的解释有积极的意义. 关键词： 变量分离法 (2+1)维非线性KdV方程 新孤子结构     

Solitons in a generalized (2+1)-dimensional Ablowitz－Kaup－Newell－Segur system

In the previous Letter (Zheng C L and Zhang J F 2002 Chin. Phys. Lett. 19 1399), a localized excitation of the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps, rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations, which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.     

Fractal Dromion, Fractal Lump, and Multiple Peakon Excitations in a New (2+1)-Dimensional Long Dispersive Wave System

By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: λqt + qxx - 2q ∫ (qr)xdy ＝ 0, λrt - rxx + 2r ∫(qr)xdy ＝ 0, is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, farctal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.     

(2+1)维破裂孤子方程的多方孤子解及其混沌行为

利用投射方程法和变量分离法,得到(2+1)维破裂孤子方程的新显式精确解. 根据得到的孤立波解,利用 Weierstrassp 函数,构造出多方孤子局域结构. 利用两个混沌系统研究了破裂孤子方程的混沌行为. 关键词： 投射方程法 破裂孤子方程 多方孤子 混沌行为     

New Exact Solutions of （1 ＋ 1）-Dimensional Coupled Integrable Dispersionless System

This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed.     

(2+1)维Boiti-Leon-Pempinelle系统的钟状和峰状圈孤子

借助于Painlev Bcklund变换和多线性变量分离方法, 求得了(2+1)维非线性Boiti Leon Pempinelle系统的一般变量分离解．根据得到的一般解, 可以构建出丰富的局域相干结构, 如峰状孤子、紧致子等. 得到了两种新的局域结构——钟状圈孤子和峰状圈孤子, 并简要讨论了这两种圈孤子的一些特殊演化性质． 关键词： Boiti Leon Pempinelle系统 多线性变量分离法 钟状圈孤子 峰状圈孤子     

A Novel Class of Coherent Localized Structures for the Maccari System

By means of the Backlund transformation, a quite general variable separation solution of the (2 1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion,lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structurescan be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localizedstructures like peakon solution and compacton solution of this new system are found by selecting aperopriate functions.     

New exact excitations and soliton fission and fusion for the （2＋1）-dimensional Broer-Kaup-Kupershmidt system

With the help of an extended mapping approach, a series of new types of exact excitations with two arbitrary functions of the (2 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific soliton fission and fusion solutions of the higher-dimensional BKK system are also obtained.     

(1+1)维广义的浅水波方程的变量分离解和孤子激发模式

研究(1+1)维广义的浅水波方程的变量分离解和孤子激发模式. 该方程包括两种完全可积(IST可积)的特殊情况，分别为AKNS方程和Hirota-Satsuma方程. 首先把基于Bcklund变换的变量分离(BT-VS)方法推广到该方程，得到了含有低维任意函数的变量分离解. 对于可积的情况，含有一个空间任意函数和一个时间任意函数，而对于不可积的情况，仅含有一个时间任意函数，其空间函数需要满足附加条件. 另外，对于得到的(1+1)维普适公式，选取合适的函数，构造了丰富的孤子激发模式，包括单孤子，正-反孤子，孤子膨胀，类呼吸子，类瞬子等等. 最后，对BT-VS方法作一些讨论. 关键词： 浅水波方程 Bcklund变换 变量分离 孤子     

Variable Separation Solutions of Generalized Broer-Kaup System via a Projective Method

Using an extended projective method, a new type of variable separation solution with two arbitrary functions of the (2+1)-dimensional generalized Broer-Kaup system (GBK) is derived. Based on the derived variable separation solution, some special localized coherent soliton excitations with or without elastic behaviors such as dromions, peakons, and foldons etc. are revealed by selecting appropriate functions in this paper.     

A Novel Class of Coherent Localized Structures for the Maccari System

By means of the Baecklund transformation, a quite general variable separation solution of the (2 1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localized structures like peakon solution and compacton solution of this new system are found by selecting apfropriate functions.     

Coherent soliton structures of the (2+1)-dimensional long-wave－short-wave resonance interaction equation

The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave－short-wave resonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by the entrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shown that the coherent soliton structures may be dromions, solitoffs, etc.     

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.     

Engineerable generation of quadratic solitons in synthetic phase matching

We show that the efficiency and the mismatch bandwidth of quadratic soliton formation under conditions of second-harmonic generation can be enhanced in an important way in synthetic phase-matching profiles. Soliton excitation in smooth but arbitrary profiles is shown to be well described by a reduced variational approach. The potential of abrupt, nonadiabatic profiles for improved soliton formation is numerically revealed.     

Multi-valued solitary waves in multidimensional soliton systems

Considering that folded phenomena are rather universal in nature and some arbitrary functions can be included in the exact excitations of many (2+1)-dimensional soliton systems, we use adequate multivalued functions to construct folded solitary structures in multi-dimensions. Based on some interesting variable separation results in the literature, a common formula with arbitrary functions has been derived for suitable physical quantities of some significant (2+1)-dimensional soliton systems like the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) model, the generalized Nizhnik－Novikov－Veselov (GNNV) system and the new (2+1)-dimensional long dispersive wave (NLDW) system. Then a new special type of two-dimensional solitary wave structure, i.e. the folded solitary wave and foldon, is obtained. The novel structure exhibits interesting features not found in the single valued solitary excitations.