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Bifurcations of traveling wave solutions and exact solutions to generalized Zakharov equation and Ginzburg-Landau equation

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Applied Mathematics and Mechanics(English Edition) 2011年第12期32卷 1615-1622页

作者：戴振祥徐园芬 School of Information and Art Ningbo Institute of Education Junior College Zhejiang Wanli University

This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given.

关键词： planar dynamical system periodic wave solution nonlinear wave equation

Z_2-Equivariant Cubic system Which Yields 13 Limit Cycles

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 781-800页

作者： Yi-rong LIU Ji-bin LI School of Mathematics Central South University Department of Mathematics Zhejiang Normal University School of Science Kunming University of Science and Technology

For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.

关键词： planar dynamical system limit cycles bifurcations Lyapnov constant weak focus

Bifurcations of Exact Traveling Wave Solutions for(2+1)-Dimensional HNLS Equation

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Communications in Theoretical Physics 2012年第1期57卷 68-70页

作者： XU Yuan-Fen Junior College Zhejiang Wanli UniversityNingbo 315101China

For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the metho... 详细信息

关键词： planar dynamical system periodic wave solution solitary wave solution (2+1)-DimensionalHNLS equation

dynamical understanding of loop soliton solution for several nonlinear wave equations

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Science China Mathematics 2007年第6期50卷 773-785页

作者： Ji-bin LI Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China Kunming University of Science and Technology, Kunming 650093, China Department of Mathematics Zhejiang Normal University Jinhua China Kunming University of Science and Technology Kunming China

It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.

关键词： planar dynamical system homoclinic orbit solitary wave solution one-loop soliton solution periodic wave solution bifurcation nonlinear wave equation 34C37 34C23 74J30 58Z05

Shape Analysis and Solution to a Class of NonlinearWave Equation with Cubic Term

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Advances in Applied Mathematics and Mechanics 2012年第5期4卷 559-574页

作者： Xiang Li Weiguo Zhang Yan Zhao College of Science University of Shanghai for Science and TechnologyShanghai 200093China School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjingJiangsu 210044China

In this paper,we analyze the relation between the shape of the bounded traveling wave solutions and dissipation coefficient of nonlinear wave equation with cubic term by the theory and method of planar dynamical *** critical values which can characterize the scale of dissipation effect are *** dissipation effect is not less than a certain critical value,the traveling wave solutions appear as kink profile;while if it is less than this critical value,they appear as damped *** expressions of bounded traveling wave solutions are presented,including exact expressions of bell and kink profile solitary wave solutions,as well as approximate expressions of damped oscillatory *** approximate damped oscillatory solution,using homogenization principle,we give its error estimate by establishing the integral equation which reflects the relations between the exact and approximate *** can be seen that the error is an infinitesimal decreasing in the exponential form.

关键词： Nonlinear wave equation planar dynamical system exact solutions approximate damped oscillatory solutions error estimate