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Variable Separated Solutions and Four-Dromion Excitations for (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation

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Communications in Theoretical Physics 2008年第3期49卷 679-684页

作者： HU Ya-Hong ma zheng-yi zheng Chun-Long College of Science Zhejiang Lishui University Lishui 323000 China Shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China

Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed.

关键词： Imapping approach Nizhnik-Novikov-Veselov equation variable separated solution dromion

A Note on "Doubly Periodic Propagating Wave for (2+1)-Dimensional Breaking Soliton Equation"

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Communications in Theoretical Physics 2009年第1期51卷 79-80页

作者： zheng Chun-Long PAN Zhen-Huan ma zheng-yi School of Physics and Mechanical Engineering Shaoguan University Shaoguan 512005 China College of mathematics and Physics Lishui University Lishui Zhejiang 323000 China Shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China

In a recent paper [Commun. Theor. Phys. （Beijing, China） 49 （2008） 268], Huang et al. gave a general variable separation solution to the （2＋1）-dimensional breaking soliton equation via a special Biicldund transformation and the variable separation approach. In terms of the derived variable separation solution and by introducing Jacobi elliptic functions, they claimed that nonelastic types of interaction between Jacobi elliptic function waves are investigated both analytically and graphically. We show that some inappropriateness or errors exist in their paper, and say nothing of the conclusion that some nonelastic types of interaction between Jacobi elliptic function waves in the （2＋1）-dimensional breaking soliton equation have been found.

关键词： breaking soliton equation variable separation solution interaction comment

Doubly Periodic Propagating Wave Patterns of （2＋1）-Dimensional maccari System

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Communications in Theoretical Physics 2007年第3期47卷 397-402页

作者： HUANG Wen-Hua LIU Yu-Lu ma zheng-yi College of Science Zhejiang Huzhou University Huzhou 313000 China Shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China College of Science Zhejiang Lishui University Lishui 323000 China

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.

关键词： maccari system variable separation method Jacobi elliptic function periodic wave

Solitons and Waves in （2＋l）-Dimensional Dispersive Long-Wave Equation

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Communications in Theoretical Physics 2006年第5X期46卷 799-803页

作者： ma zheng-yi LIU Yu-Lu LU Zhi-Ming zheng Chun-Long2LU Zhi-Ming,1 and zheng Chun-Long Shaaghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China Department of mathematics Zhejiang Lishui University Lishui 323000 China

For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.

关键词： (2+l)-dimensional dispersive long-wave equation projective Riccati equation approach soliton annihilation traveling wave

Analytical solutions and rogue waves in （3+1）-dimensional nonlinear Schrdinger equation

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Chinese Physics B 2012年第3期21卷 138-144页

作者：马正义马松华 College of mathematics and Physics Zhejiang Lishui University

Analytical solutions in terms of rational-like functions are presented for a（3+1）-dimensional nonlinear Schrdinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct *** free functions of time t are involved to generate abundant wave *** types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.

关键词： nonlinear Schrdinger equation similarity transformation rational-like solution rogue

New Exact Solutions to (2+1)-Dimensional Variable Coefficients Broer-Kaup Equations

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Communications in Theoretical Physics 2006年第9期46卷 393-396页

作者： ZHU Jia-Min~(1,2,+) ma zheng-yi~(1,2) ~1 Department of Physics, Zhejiang Lishui University, Lishui 323000, China ~2 Shanghai Institute of Applied mathematics and Mechanics, Shanghai 200072, China Department of Physics Zhejiang Lishui University Shanghai Institute of Applied mathematics and Mechanics

In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.

关键词： variable coefficient generalized projected Ricatti equation method (2+1)-dimensional variable coefficients Broer Kaup equations Weierstrass function solution solitary wave solution trigonometric function solution

Hybrid-Lattice系统和Ablowitz-Ladik-Lattice系统的新解探索

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物理学报 2005年第2期54卷 483-489页

作者：朱加民马正义郑春龙丽水学院物理系丽水323000

对tanh函数方法进行了对称延拓 ,并拓广了它的应用范围 ,将其应用于非线性离散系统的求解 .研究了Hybrid Lattice系统和Ablowitz Ladik Lattice系统 .

关键词：周期波解孤波解拓广求解对称延拓非线性离散系统函数方法 e系统研究

Riccati方程与(2+1)维非线性物理模型的分离变量解

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数学的实践与认识 2005年第12期35卷 170-173页

作者：马正义浙江丽水学院数学系

对于(2+1)维非线性物理模型,欲获其解并非易事.本文试图在变量分离法中,通过设定的R iccati方程来得到方程的解.同时,以(2+1)维Bo iti-L eon-M anna-P em p inelli方程和Burgers方程为例来说明之.

关键词：非线性物理模型变量分离法 Riccati方程

Solitons for the cubic-quintic nonlinear Schrdinger equation with varying coefficients

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Chinese Physics B 2012年第5期21卷 133-139页

作者：陈元明马松华马正义 College of Sciences Lishui University

In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of *** types of free f... 详细信息

关键词： cubic-quintic nonlinear SchrSdinger equation similarity transformation explicit solu-tions