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Exact traveling wave solutions for an integrable nonlinear evolution equation given by ***

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Applied Mathematics and Mechanics(English Edition) 2008年第4期29卷 437-440页

作者：李继彬 School of Science .Kunming University of Science and Technology Department of Mathematics Zhejiang Normal UniversityJinhua 321004Zhejiang ProvinceP.R.China

By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave... 详细信息

关键词： solitary wave solution periodic wave solution kink and anti-kink wave solutions nonlinear evolution equation

Localized Excitations in a Sixth-Order （1＋1）-Dimensional nonlinear evolution equation

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Communications in Theoretical Physics 2005年第6X期44卷 961-963页

作者： SHEN Shou-Feng Department of Mathematics Zhejiang University of Technology Hangzhou 310014 China

In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.

关键词： variable separation Lax pair Darboux transformation nonlinear evolution equation localized excitation

Generalized Dromion Structures of New（2＋1）—Dimensional nonlinear evolution equation

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Communications in Theoretical Physics 2001年第3期35卷 267-270页

作者： ZHANGJie－Fang InstituteofnonlinearPhysics ZhejiangNormalUniversityJinhua321004ZhejiangProvinceChina

We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this... 详细信息

关键词： (2+1) dimensions nonlinear evolution equation soliton dromion

Stability of planar diffusion wave for nonlinear evolution equation Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Science China Mathematics 2012年第2期55卷 337-352页

作者： HE Cheng HUANG FeiMin YONG Yan National Natural Science Foundation of China Beijing 100085China Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China College of Science University of Shanghai for Science and TechnologyShanghai 200093China

It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u）〉 0, u（±∞, t）： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.

关键词： stability planar diffusion wave nonlinear evolution equation

Travelling Wave Solutions to a Special Type of nonlinear evolution equation

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Communications in Theoretical Physics 2003年第1期39卷 39-43页

作者： XUGui－Qiong LIZhi－Bin DepartmentofComputerScience EastChinaNormalUniversityShanghai200062China；DepartmentofInformationAdministrationShanghaiUniversityShanghai200436China DepartmentofComputerScience Ea

A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbitrariness of the manifold in Painlevé analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.

关键词： Painleve analysis rank travelling wave solution nonlinear evolution equation

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Applied Mathematics and Mechanics(English Edition) 2002年第4期23卷 380-386页

作者：谢福鼎闫振亚张鸿庆 Department of Applied Mathematics Dalian University of Technology Dalian P R China

Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct met... 详细信息

关键词： nonlinear evolution equation FPU problem similarity reduction

On the Asymptotic Property of Solution for Some nonlinear evolution equation of Second Order

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Journal of Mathematical Research and Exposition 2004年第1期24卷 44-48页

作者：叶耀军河南农业大学信息与计算科学系

In the article we show the decay of the solution for some nonlinear evolution equation of second order by using a difference inequality.

关键词： nonlinear evolution equation initial-boundary value problem decay property of global solution.

Trial equation Method to nonlinear evolution equations with Rank Inhomogeneous： Mathematical Discussions and Its Applications

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Communications in Theoretical Physics 2006年第2期45卷 219-223页

作者： LIU Cheng-Shi Department of Mathematics Daqing Petroleum Institute Daqing 163318 China

A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As appncations, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation, generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.

关键词： trial equation method solvable equation nonlinear evolution equation exact solution

STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR nonlinear DISSIPATIVE evolution equationS IN BANACH SPACE

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Journal of Computational Mathematics 2024年第2期42卷 337-354页

作者： Wansheng Wang Department of Mathematics Shanghai Normal UniversityShanghai 200234China

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach *** break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are *** employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative *** applications of the main results to several linear multistep methods,including the trapezoidal rule,are *** theoretical results are also illustrated by a set of numerical experiments.

关键词： nonlinear evolution equation Linear multistep methods ω-dissipative operators Stability Convergence Banach space