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Communications in Computational Physics 2011年第10期10卷 1257-1279页

作者： Ravi Kannan CFD Research Corporation 215Wynn DriveHuntsvilleAL 35805USA

In this paper,we develop a formulation for solving equations containing higher spatial derivative terms in a spectral volume(SV)context;more specifically the emphasis is on handling equations containing third derivative terms.This formulation is based on the LDG(Local Discontinuous Galerkin)flux discretization method,originally employed for viscous equations containing second derivatives.A linear Fourier analysis was performed to study the dispersion and the dissipation properties of the new formulation.The Fourier analysis was utilized for two purposes:firstly to eliminate all the unstable SV partitions,secondly to obtain the optimal SV partition.Numerical experiments are performed to illustrate the capability of this formulation.Since this formulation is extremely local,it can be easily parallelized and a h-p adaptation is relatively straightforward to implement.In general,the numerical results are very promising and indicate that the approach has a great potential for higher dimension Korteweg-de Vries(kdv)type problems.

关键词： Spectral volume LDG higher spatial derivative terms kdv Fourier analysis

Generation of solitary waves in a three-layer fluid system

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Science China Mathematics 1995年第10期38卷 1239-1245页

作者：朱勇 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

Based on the generalized Boussinesq equations for the three-layer fluid system, the kdv equations for the interfaces are obtained by using a perturbation method and the effect of fluid depth on the generation of solitary waves is discussed. By classifying the waves into fast-, medium- and slow-modes, it is found that the results on the slow-mode waves is qualitatively consistent with the experimental ones, and there may exist concave solitary waves on free surface, which is yet to be verified by experiments.

关键词： solitary waves stratified fluid kdv eqration.

NUMERICAL SOLUTION OF AN INITIALBOUNDARY VALUE PROBLEM OF THE KORTEWEG-DE VRIES EQUATION

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Acta Mathematica Scientia 1985年第3期5卷 337-348页

作者：郭本瑜 Dept. of Math. University of Science and Technology of Shanghai Shanghai China

An initial-boundary value problem of the Korteweg-de Vries equation is considered. A conservation law fox this problem is derived. A difference scheme is introduced and its conservation property is compared to the conservation law. The convergence of this scheme is strictly proved. It is shown numerically that such scheme is applicable. Numerical results for the case where the initial condition is zero and the boundary condition is a rectangle pulse are also obtained. It is found that the solution exhibits soliton-like behaviour.

关键词： kdv NUMERICAL SOLUTION OF AN INITIALBOUNDARY VALUE PROBLEM OF THE KORTEWEG-DE VRIES EQUATION

PSEUDOPOTENTIAL METHOD APPLIED TO kdv EQUATION AND HIGHER DEGREE kdv EQUATION

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Acta Mathematica Scientia 1984年第3期4卷 319-324页

作者：潘祖梁 Zhejiang University

In this paper,pseudopotential method is applied to kdv equation and higher degree kdv equation. For kdv equation we find the relative connection between pseudopotential and various travelling wave solutions of kdv equation, i. e. the discontinuous solution, the unbounded periodic solution and the soliton-like solution of kdv equation are determined by zero of pseudopotential function. The pseudopotential and solitary wave solution of the higher degree kdv equation and n-dimension higher degree kdv equation are presented.

关键词：切二 real kdv PSEUDOPOTENTIAL METHOD APPLIED TO kdv EQUATION AND HIGHER DEGREE kdv EQUATION

EXPLICIT EXACT SOLUTIONS TO A GENERALIZED kdv EQUAFION

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数学物理学报（A辑） 1997年第S1期17卷 168-174页

作者：马文秀周德常

This paper carefully analyses the possibility of that a generalized kdv equa- tion possesses a family of solutions of the finite series form,and thus a kind of its explicit complex exact solutions is cxhibited.These complex solutions constitute real exact so- lutions to th e system of complex form of the above generalized kdv equation.

关键词： Generalized kdv equation travelling wave solution series method

SUPERPOSITION FORMULAE OF A FIFTH ORDER kdv EQUATION AND ITS MODIFIED EQUATION

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Acta Mathematicae Applicatae Sinica 1988年第1期4卷 46-54页

作者：胡星标李勇 Tongji University

The Backlund transformation (BT) for a fifth order kdv equation is presented in the bilinear form.Furthermore,a nonlinear superposition formula related to the BT obtained above is proved rigorously.By the way,a nonlin... 详细信息

关键词： kdv ED SUPERPOSITION FORMULAE OF A FIFTH ORDER kdv EQUATION AND ITS MODIFIED EQUATION EQ 知一 BT ITS

Variable Coefficient kdv Equation for Amplitude of Nonlinear Solitary Rossby Waves in a Sort of Time-Dependent Zonal Flow

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高原气象 2011年第2期30卷 349-354页

作者： DA Chao-jiu SUN Shu-peng SONG Jian YANG Lian-gui College of Atmospheric Sciences Lanzhou University Lanzhou 730000 China School of Mathematics and Computer Science Institute Northwest University for Nationalities Lanahou 730124 China College of Science Inner Mongolia University of Technology Hohhot 010062 China School of Mathematical Sciences Inner Mongolia University Hohhot 010021 China)

On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion tha... 详细信息

关键词： Nonlinear Rossby Waves Variable coefficient kdv equation Time-dependent zonal flow Perturbation method

SOME PROPERTIES OF SOLITON IN NON-CLASSICAL VARIATION FIELD

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Acta Mathematica Scientia 1983年第4期3卷 369-375页

作者：张学铭 Institute of Applied Mathematics Zhejiang University~1 Wuhan Institute of Mathematical Sciences Academia Sinica

This paper is concerned with some characteristc properties of soliton by utilizing nonclassical variational methods. [1-3] We discussed short range of soliton and the stability of soliton) of kdv equation. The main re... 详细信息

关键词： SOME PROPERTIES OF SOLITON IN NON-CLASSICAL VARIATION FIELD kdv

A BETTER DIFFERENCE SCHEME WITH FOUR NEAR-CONSERVED QUANTITIES FOR THE kdv EQUATION

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Journal of Computational Mathematics 1994年第3期12卷 224-234页

作者： Han Zhen (Computing Center Academia Sinica Beijing China)Shen Long-jun(Institute of Applied Physics and Computational Mathematics, Beijing, China) 中科院计算数学与科学工程计算所北京北京应用物理和计算数学所北京

In this paper, we present a new semi-discrete difference scheme for the kdv equation, which possesses the first four nearconserved quatities. The scheme is better than the past one given in [4], because its solution ... 详细信息

关键词： kdv A BETTER DIFFERENCE SCHEME WITH FOUR NEAR-CONSERVED QUANTITIES FOR THE kdv EQUATION EH

EQUATORIAL SOLITARY WAVES OF TROPICAL ATMOSPHERIC MOTION IN SHEAR FLOW

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Advances in Atmospheric Sciences 1987年第2期4卷 125-136页

作者：李麦村 Academia Sinica Beijing Institute of Atmospheric Physics

Starting from the primary equations, the author derives the kdv equation which describes solitary Rossby waves in the tropical atmosphere, and indicates that, because these waves are ageostrophic, they differ from the quasigeostrophic solitary Rossby waves studied by Redekopp et al. Owing to nonlinear action, these waves are also different from traditional linear waves of the tropical atmosphere. The author believes that the stationary tropical atmospheric waves reflect the characteristics of solitary waves in that the energy does not disperse.

关键词： EQUATORIAL SOLITARY WAVES OF TROPICAL ATMOSPHERIC MOTION IN SHEAR FLOW kdv