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Exact Solutions of Some （1＋1）-Dimensional Nonlinear Evolution Equations

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Communications in Theoretical Physics 2006年第2期45卷 236-238页

作者： shen shou-feng Department of Mathematics Zhejiang University of Technology Hangzhou 310014 China

By means of the variable separation method, new exact solutions of some （1 ＋ 1）-dimensionaJ nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.

关键词： variable separation Ito equation AKNS equation Hirota-Satsuma equation localized excitation

Multi-linear Variable Separation Approach to Solve a （1＋1）-Dimensional Coupled Integrable Dispersionless System

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Communications in Theoretical Physics 2005年第5X期44卷 779-782页

作者： shen shou-feng Department of Mathematics Zhejiang University of Technology Hangzhou 310014 China

The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+ 1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-less ***, by using a Backlund transformation and the MLVSA, we find a new general solution and define a new "universal formula". Then, some new (1+1)-dimensional coherent structures of this universal formula can be found by selecting corresponding functions appropriately. Specially, in some conditions, bell soliton and kink soliton can transform each other, which are illustrated graphically.

关键词： variable separation approach (1+1)-dimensional coupled integrable dispersion-less system co-erent structure

Clarkson-Kruskal Direct Similarity Approach for Differential-Difference Equations

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Communications in Theoretical Physics 2005年第6X期44卷 964-966页

作者： shen shou-feng Department of Mathematics Zhejiang University of Technology Hangzhou 310014 China

In this letter, the Clarkson-Kruskal direct method is extended to similarity reduce some differentialdifference equations. As examples, the differential-difference KZ equation and KP equation are considered.

关键词： differential-difference KZ equation differential-difference KP equation direct method similarity reduction

Localized Excitations in a Sixth-Order （1＋1）-Dimensional Nonlinear Evolution Equation

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Communications in Theoretical Physics 2005年第6X期44卷 961-963页

作者： shen shou-feng Department of Mathematics Zhejiang University of Technology Hangzhou 310014 China

In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.

关键词： variable separation Lax pair Darboux transformation nonlinear evolution equation localized excitation

Soliton Motion in （1＋1）-Dimensions

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Communications in Theoretical Physics 2006年第1期45卷 41-44页

作者： ZHANG Jun shen shou-feng Department of Mathematics Zhejiang University of Technology Hangzhou 310014~ China

By using the variable separation approach, which is based on the corresponding Backlund transformation, new exact solutions of a （1＋1）-dimensional nonlinear evolution equation are obtained. Abundant new soliton mot... 详细信息

关键词： Backlund transformation variable separation nonlinear evolution equation soliton

Rellich type inequalities related to Grushin type operator and Greiner type operator

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Applied Mathematics(A Journal of Chinese Universities) 2012年第3期27卷 353-362页

作者： shen shou-feng JIN Yong-yang Department of Applied Mathematics Zhejiang University of TechnologyHangzhou 310032China

We prove some sharp Hardy inequality associated with the gradient △γ=（△x,｜x｜γ [x△y） by a direct and simple approach. Moreover, similar method is applied to ob- tain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L^p. We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators.

关键词： Rellich inequality Hardy inequality Grushin type operator Greiner type operator.

New Exact Solutions of the N-Coupled Nonlinear Schroedinger System

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Communications in Theoretical Physics 2005年第4X期44卷 604-608页

作者： shen shou-feng ZHANG Jun YE Cai-Er PAN Zu-Liang Department of Mathematics Zhejiang University of Technology Hangzhou 310014 China Basic Department Zhejiang Forestry College Lin'an 311300 China Department of Mathematics Zhejiang University Hangzhou 310027 China

In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions.

关键词： nonlinear Schroedinger system exact solution Jacobi elliptic function soliton

(1+1)维广义的浅水波方程的变量分离解和孤子激发模式

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物理学报 2006年第3期55卷 1016-1022页

作者：沈守枫浙江工业大学数学系杭州310014

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Backlund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... 详细信息

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Backlund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：水波方程 Backlund变换变量分离孤子

低维非线性系统的一般多线性变量分离方法和局域激发模式

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物理学报 2006年第3期55卷 1011-1015页

作者：沈守枫浙江工业大学数学系杭州310014

基于Backlund变换的多线性变量分离方法(BT_MLVSA)是求解非线性系统的一种非常有效的方法.一般多线性变量分离方法(GMLVSA)是该方法的推广.实现GMLVSA主要有四种途径,一是先把场量按照多个任意函数(通常考虑两个函数的情形)展开得到关... 详细信息

基于Backlund变换的多线性变量分离方法(BT_MLVSA)是求解非线性系统的一种非常有效的方法.一般多线性变量分离方法(GMLVSA)是该方法的推广.实现GMLVSA主要有四种途径,一是先把场量按照多个任意函数(通常考虑两个函数的情形)展开得到关于多个函数的多线性方程,另一种途径是推广变量分离的假设,第三类是基于Darboux变换的多线性变量分离方法(DT_MLVSA),第四类是导数相关泛函变量分离法.利用第一类GMLVSA,可以得到(2+1)维mNNV系统和sine_Gordon系统的一般多线性变量分离解.把第一类GMLVSA推广到二维非线性系统,这些系统是通过对称约化(2+1)维sine_Gordon.系统得到的.也就是说,一般多线性变量分离可解性在对称约化下从高维系统到低维系统得到了保持.这也提供了一条从高维非线性系统导出可GMLVSA求解的低维非线性系统的有效途径.

关键词： Backlund变换多线性变量分离 sine-Gordon系统对称约化