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The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

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Chinese Physics B 2007年第7期16卷 1848-1854页

作者：马正义 College of Mathematics and Physics Zhejiang Lishui University Lishui 323000 China

Using the projective Riccati equation expansion （PREE） method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.

关键词： projective Riccati equation nonlinear physical equation variable separation solution soliton

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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

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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

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