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Exact Solutions to Nonlinear Schr(?)dinger Equation and Higher-Order Nonlinear Schr(?)dinger Equation

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Communications in Theoretical Physics 2008年第9期50卷 575-578页

作者： REN Ji ruan hang-yu Department of Physics Ningbo University Ningbo 315211 China

We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.

关键词： generalized Lie group reduction method nonlinear Schroedinger equation higher order nonlin ear Schroedinger equation

Restudy of Structures and Interactions of Solitons in （2＋1）-Dimensional Nizhnik-Novikov-Veselov Equations

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Communications in Theoretical Physics 2006年第1期45卷 1-8页

作者： ruan hang-yu CHEN Yi-Xin Institute of Modern Physics Ningbo University Ningbo 315211 China Zhejiang Institute of Modern Physics Zhejiang University Hangzhou 310027 China

Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our results. Detailed behaviors of interaction are illustrated both analytically and in graphically. Our analysis shows that the interaction properties between two solitons are related to the form of interaction constant. The form of interaction constant and the dispersion relationship are related to the form of the seed solution （u0, v0, w0 ） in Backlund transformation.

关键词： interaction between two solitons bilinear approach seed solution NNV equation

Interaction Between Line Soliton and Algebraic Soliton for Asymmetric Nizhnik-Novikov-Veselov Equation

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Communications in Theoretical Physics 2008年第6期49卷 1547-1552页

作者： ruan hang-yu LI Zhi-Fang Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.

关键词： variable separation approach the interaction between line soliton and algebraic soliton (2+1)-dimensional ANNV equation

A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations

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Communications in Theoretical Physics 2009年第11期52卷 801-807页

作者： YANG Xu-Dong ruan hang-yu Department of Physics Ningbo University Ningbo 315211 China

An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations withlogarithmic transformations is *** the algorithm,the general assumption of Hirota bilinear form is successfullyreduced based on the property of uniformity in ***,we discard the integral operation in the *** software package HBFTrans is written in Maple and its running effectiveness is tested by a variety solitonequations.

关键词： Hirota bilinear form nonlinear equation, symbolic algebra

Conformal Invariant Asymptotic Expansion Approach for Solving （3＋1）-Dimensional JM Equation

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Communications in Theoretical Physics 2006年第6期45卷 979-984页

作者： LI Zhi-Fang ruan hang-yu Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.

关键词： (3+1)-dimensional Jimbo-Miwa (JM) equation conformal invariant asymptotic expansion approach Painlevé property approximate and exact solutions

Infinitely Many Symmetries of Konopelchenko-Dubrovsky Equation

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Communications in Theoretical Physics 2005年第3X期44卷 385-388页

作者： LI Zhi-Fang ruan hang-yu Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department of Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lo... 详细信息

关键词： formal function series method Konopelchenko-Dubrovsky equation infinite dimensional generalized ω∞ algebra

An Extension of Algorithm on Symbolic Computations of Conserved Densities for High-Dimensional Nonlinear Systems

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Communications in Theoretical Physics 2008年第7期50卷 23-30页

作者： YANG Xu-Dong ruan hang-yu LOU Sen-yue Department of Physics Ningbo University Ningbo 315211 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

An improved algorithm for symbolic computations of polynomial-type conservation laws (PCLaws) of ageneral polynomial nonlinear system is *** algorithm is implemented in Maple and can be successfully usedfor high-dimensional ***,the algorithm discards the restriction to evolution *** programcan also be used to determine the preferences for a given parameterized nonlinear *** code is tested on severalknown nonlinear equations from the soliton theory.

关键词： conservation laws nonlinear systems computer algebra

A Maple Package on Symbolic Computation of Conserved Densities for （1＋l）-Dimensional Nonlinear Evolution Systems

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Communications in Theoretical Physics 2007年第6期47卷 961-968页

作者： YANG Xu-Dong ruan hang-yu LOU Sen-yue Department of Physics Ningbo University Ningbo 315211 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

A new algorithm for symbolic computation of polynomial-type conserved densities for nonlinear evolution systems is presented. The algorithm is implemented in Maple. The improved algorithm is more efficient not only in removing the redundant terms of the genera/form of the conserved densities but also in solving the conserved densities with the associated flux synchronously without using Euler operator. Furthermore, the program *** can be used to determine the preferences for a given parameterized nonlinear evolution systems. The code is tested on several well-known nonlinear evolution equations from the soliton theory.

关键词： conservation laws nonlinear evolution systems computer algebra

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可积模型中孤子相互作用的研究

物理学报 2001年第3期50卷 369-376页

作者：阮航宇宁波大学物理系

从可积模型的双线性形式出发 ,可以得到关于方程场变量或某种势所存在的所有方向都是指数局域的dromion解或除一个方向外指数衰减的“Solitoff”解 .以 (1+ 1)维和 (2 + 1)维KdV类型方程为例 ,对孤子 (dromions或“Solitoff”)间的相互... 详细信息

从可积模型的双线性形式出发 ,可以得到关于方程场变量或某种势所存在的所有方向都是指数局域的dromion解或除一个方向外指数衰减的“Solitoff”解 .以 (1+ 1)维和 (2 + 1)维KdV类型方程为例 ,对孤子 (dromions或“Solitoff”)间的相互作用进行了详细的研究 ,发现孤子间的相互作用规律与方程的维数和类型无关 .只要方程的多孤子解形式符合Hirota标准形式 (所有耦合系数均不为零 ) ,孤子之间的碰撞是弹性的。

关键词：可积模型孤子相互作用双线性方法 Kdv方程 ANNV方程