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Influence of dissipation on solitary wave solution to generalized Boussinesq equation

Applied Mathematics and Mechanics(English Edition) 2023年第3期44卷 477-498页

作者： Weiguo ZHANG Siyu HONG Xingqian LING Wenxia LI College of Science University of Shanghai for Science and TechnologyShanghai 200093China

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations,and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary *** dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in *** influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied,and the critical values that can describe the magnitude of the dissipation effect are,respectively,found for the two cases of b_30 in the *** results show that,when the dissipation effect is significant(i.e.,r is greater than the critical value in a certain situation),the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution;when the dissipation effect is small(i.e.,r is smaller than the critical value in a certain situation),the traveling wave solution to the equation appears as the oscillation attenuation *** using the hypothesis undetermined method,all possible solitary wave solutions to the equation when there is no dissipation effect(i.e.,r=0)and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained;in particular,when the dissipation effect is small,an approximate solution of the oscillation attenuation solution can be *** paper is further based on the idea of the homogenization *** establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper,and by investigating the asymptotic behavior of the solution at infinity,the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained,which is an infinitesimal amount that decays *** influ

关键词： generalized Boussinesq equation influence of dissipation qualitative analysis solitary wave solution oscillation attenuation solution error estimation

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New Exact and Explicit solitary wavesolutions to a Class of Coupled Nonlinear Equations

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 189-193页

作者： Xuejun XU and Jiefang ZHANG(Institute of Nonlinear Physics and Dept. of Physics. Zhejiang Normal Univ., Jinhua321004, China) Institute of Nonlinear Physics and Department of Physics Zhejiang Normal University Jinhua 321004 China

New exact and explicit solitary wave solutions are obtained for the couplednonlinear equation by using a simple way of making the ansatz u(x, t) =Asechn ζ+A0with ζ = k(x+wt) +ζ0.

关键词： solitary wave solution ansatz coupled nonlinear equations

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A polynomial Expansion Method and New General solitary wave solutions to KS Equation

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Communications in Theoretical Physics 2003年第6期39卷 641-642页

作者： PENGYan-Ze LaboratoryofpureandAplliedMathematics CCSESchoolofMathematicalSciencesPekinguniversityBeijing100871China

Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolu... 详细信息

关键词： KS equation solitary wave solution polynomial expansion method

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ON A NEW ALGORITHM OF CONSTRUCTING solitary wave solutionS FOR SYSTEMS OF NONLINEAR EVOLU-TION EQUATIONS IN MATHEMATICAL PHYSICS

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Applied Mathematics and Mechanics(English Edition) 2000年第4期21卷 383-388页

作者：闫振亚张鸿庆 Institute of Mathematical Science Dalian University of Technology Dalian 116024 China

According to the improved sine-cosine method and Wu-elimination method, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward. The algorithm has some conclusions which are better than what the hyperbolic function method known does and simpler in use. With the aid of MATHEMATICA, the algorithm can be carried out in computer.

关键词： system of nonlinear evolution equations sine-cosine method Wu-elimination method solitary wave solution

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Some New solitary wave solutions to a Compound KdV-Burgers Equation

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Communications in Theoretical Physics 2008年第7期50卷 51-52页

作者： GONG Lun-Xun PAN Jun-Ting School of Science Guizhou Normal University Guiyang 550001 China

Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f （ξ）, is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations.

关键词： traveling wave solutions compound KdV-Burgers equation solitary wave solution

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New Explicit Rational solitary wave solutions for Discretized mKdV Lattice Equation

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Communications in Theoretical Physics 2005年第6X期44卷 1011-1014页

作者： YU Ya-Xuan WANG Qi ZHANG Hong-Qing Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Key Laboratory of Mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co... 详细信息

关键词： differential-difference equations discretized mKdV lattice equation solitary wave solution rational expand method

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Abundant general solitary wave solutions to the family of KdV type equations

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Journal of Ocean Engineering and Science 2017年第1期2卷 47-54页

作者： Md.Azmol Huda M.Ali Akbar Shewli Shamim Shanta Mathematics Discipline Khulna UniversityKhulnaBangladesh Department of Applied Mathematics University of RajshahiRajshahiBangladesh Department of Mathematics University of RajshahiRajshahiBangladesh

This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations(NLEEs)through the application of the(G/G,1/G)-expansion *** method is allied to the widely used(G/G)-method initiated by Wang et *** can be considered as an extension of the(G/G)-expansion *** effectiveness,the method is applied to the family of KdV type *** general form solitary wave solutions as well as periodic solutions are successfully obtained through this ***,in the obtained wider set of solutions,if we set special values of the parameters,some previously known solutions are *** approach of this method is simple and elegantly *** been computerized it is also powerful,reliable and effective.

关键词： Nonlinear evolution equation solitary wave solution Potential KdV equation Complex modified KdV equation

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New solitary wave solutions for nonlinear evolution equations

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Chinese Physics B 2002年第9期11卷 864-868页

作者：姚若侠李志斌等 DepartmentofComputerScience EastChinaNormalUniversityShanghai200062China

Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system, Maple,using the direct algebraic method proposed recently. We explicitly obtain several new solutions of physi... 详细信息

关键词： nonlinear evolution equation Riccati equations solitary wave solution symbolic computation

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A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

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Chinese Physics B 2007年第12期16卷 3589-3594页

作者：杨红丽宋金宝杨联贵刘永军 Institute of Oceanology Chinese Academy of Sciences Qingdao 266071 China Graduate School Chinese Academy of Sciences Beijing 100049 China Department of Mathematics Inner Mongolia University Hohhot 010021 China

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters： the nonlinearity ratio ε, represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O（μ^2）. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

关键词： two-fluid system interracial waves extended KdV equation solitary wave solution

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A unified approach in seeking the solitary wave solutions to sine-Gordon type equations

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Chinese Physics B 2005年第7期14卷 1303-1306页

作者：谢元喜唐驾时 DepartmentofEngineeringMechanics HunanUniversityChangsha410082China

By utilizing the solutions of an auxiliary ordinary differential equation introduced in this paper, we present a simple and direct method to uniformly construct the exact solitary wave solutions for sine-Gordon type *** illustrative examples, the exact solitary wave solutions of some physically significant sine-Gordon type equations,including the sine-Gordon equation, double sine-Gordon equation and mKdV-sine-Gordon equation, are investigated by means of this method.

关键词： auxiliary ordinary differential equation solitary wave solution sine-Gordon type equations

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