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Wu Method and Its Application about Partial Differential Equations

Author: XiaTieCheng
Tutor: ZhangHongQing
School: Dalian University of Technology
Course: Computational Mathematics
Keywords: Characteristic set Nonlinear evolution equations Nonlinear wave equations Wu algebraic elimination not Exact solution Traveling wave solutions Solitary wave solutions Periodic solution Have to understand dromion solution Soliton solution Class multi- soliton solution C-D pairs Backlund transformation Cole-Hopf transformation Homogeneous balance method Riccati equation Separation of variables The size of the solution Appropriate solution Standard Dalian University of Technology PhD the
CLC: O241.8
Type: PhD thesis
Year: 2002
Downloads: 491
Quote: 8
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Abstract


This paper is divided into two parts, the first part discusses the theory and application of the Differential Characteristic law, related to differential equations, abstract algebra, computer algebra and other important subjects. Wu's method is applied to the physical significance of the linear partial differential equations up, we give type II sequence, verify that the appropriate solution concept given by Professor Zhang Hongqing eighties carving understand scale given in the form of power series solution. The second part of the structural transformation and symbolic computation, especially (Wu algebra elimination method) as a tool to study some of the problems in the nonlinear evolution equations: exact solution (such as soliton solutions, periodic solutions, understanding and Jacobi elliptic function solutions, doubly periodic solutions), Backlund transformation, Hopf the transformation, dromion solution and decay structure. The second chapter describes the AC = BD mode solving PDEs and their role in the partial differential equations. First CD on CD the basic theory of integrable systems is given, then the specific study of their application. How to find the transformation is a key content of this chapter. The third chapter describes the basic theory of Wu Differential characteristic set method and its application. We apply it to linear partial differential equations up to get to know the size and form of power series solutions. Therefore validated the results of Professor Zhang Hongqing 1980s. Discussed in chapter IV hyperbolic function Reform and Its Applications. Hyperbolic functions transform derived using this method of a class of reaction-diffusion equations Brusselator reaction-diffusion equation with the exact solution of the physical, chemical, and biological significance of the equation (including singular solitary wave solutions, periodic solutions and rational function solutions ). Study the KdV, coupled KdV equation and a class of compound KdV-Burgers equation, the exact solution of a class of nonlinear evolution equations, these solutions include the singular solitary wave solutions, periodic solutions and rational function solutions. Wu algebra elimination method is the most important basic tool in the problem-solving process. Chapter consider nonlinear partial differential equations of the Jacobi elliptic function solutions (doubly periodic solutions) the exact solution mechanization algorithm: the famous sine-Gordon equation and sinh-Gordon equation, we get two Jacobi elliptic function mechanization algorithm. Called the Jacobi elliptic function expansion method, it is more effective than a sine-cosine method and sn-cn function method, hyperbolic function method and simple method. Were applied to a class of nonlinear evolution equations, Solutions for the RLW and combined KdV equation up Jacobi elliptic function solutions and other exact solutions. In chapter 6, the new applications of the homogeneous balance method applied to it the WBK equation up to get a new exact solution. Applied to the Boussinesq equation up new exact solution and Wu method combines the. Homogeneous balance method applied to BK and the DLW equation up to many decay solution and decay structure. The Riccati Method Chapter VII of the use of Dr. Yan two extended discussion BK, DLW, Kupershmidt exact solution of the equation. We have obtained a number of new solutions. At the same time, we also propose a soliton solution looking for (21) - dimensional or (31) - dimensional NLEE class mechanization algorithm, the application of this method is obtained (21) - dimensional KD equation many new classes soliton solution. Promote our algorithm Fan and S. A. Riccati method of Elwakil's.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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