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Complex Wave Excitations in Generalized Broer-Kaup System

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Communications in Theoretical Physics 2007年第4X期48卷 657-661页

作者： zheng chun-long FEI Jin-Xi College of Mathematics and Physics Lishui University Lishui 323000 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

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.

关键词： improved projective method GBK system exact solution complex wave excitation

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

Evolutional Properties of Localized Excitations for Generalized Broer-Kaup System in （2＋1） Dimensions

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Communications in Theoretical Physics 2006年第3X期46卷 461-466页

作者： zheng chun-long YE Jian-Feng XU Yuan College of Mathematics and Physics Lishui University Lishui 323000 China Basic Department Guangsha College of Applied Construction Technology Dongyang 321006 China Department of Information Engineering Lishui College of Professional Technology Lishui 323000 China

Using a special Painleve-Baecklund transformation as well as the extended mapping approach and the linear superposition theorem, we obtain new families of variable separation solutions to the （2＋1）-dimensional generalized Broer-Kaup （GBK） system. Based on the derived exact solution, we reveal some novel evolutional behaviors of localized excitations, i.e. fission and fusion phenomena in the （2＋1）-dimensional GBK system.

关键词： GBK system variable separation solution localized excitation fission fusion

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

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation

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Communications in Theoretical Physics 2002年第5期38卷 517-522页

作者： ZHANG Jie-Fang HUANG Wen-Hua zheng chun-long Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China Department of Physics Jiangxi Yichun University Yichun 336000 China Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China Department of Physics Zhejiang Lishui Normal College Lishui 323000 China

The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.

关键词： variable separation approach, coherent structures, new (2+1)-dimensional soliton equation

New Families of Exact Excitations to （2＋1）-Dimensional Toda Lattice System via an Extended Projective Approach

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Communications in Theoretical Physics 2006年第5期45卷 864-868页

作者： FANG Jian-Ping FEI Jin-Xi zheng chun-long College of Physics and Mathematics Lishui University Lishui 323000 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072China

In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.

关键词： extended projective approach DDEs Toda lattice exact solution

Explicit and Exact Solutions to N-Order Schrodinger System via an Extended Mapping Approach

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Communications in Theoretical Physics 2006年第3期45卷 483-486页

作者： ZHU Hai-Ping zheng chun- long FANG Jian-Ping Department of Physics Zhejiang Lishui University Lishui 323000 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

In this paper, we extend the mapping approach to the N-order Schrodinger equation. In terms of the extended mapping approach, new families of variable separation solutions with some arbitrary functions are derived.

关键词： extended mapping approach SchrSdinger equation exact solution

Exact Solution to （1＋1）-Dimensional Higher-Order Schrodinger Equation via an Extended Mapping Approach

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Communications in Theoretical Physics 2006年第1期45卷 127-130页

作者： ZHU Hai-Ping zheng chun-long FANG Jian-Ping Department of Physics Zhejiang Lishui University Lishui 323000 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitra... 详细信息

关键词： extended mapping approach Schrodinger equation exact solution