Dissertation > Excellent graduate degree dissertation topics show

Symmetry and Exact Solutions of the Nonlinear Partial Differential Equation

Author: DongZuoZuo
Tutor: ZhangHongQing
School: Dalian University of Technology
Course: Applied Mathematics
Keywords: Generalized conditional symmetry Initial value problem Evolution equations Exact solution
CLC: O175.29
Type: Master's thesis
Year: 2010
Downloads: 123
Quote: 0
Read: Download Dissertation

Abstract


In this paper, mathematical thinking and Professor Zhang Hongqing mechanization proposed AC = BD under the guidance of the theory by means of symbolic computation software Maple, studied the symmetry method for solving nonlinear partial differential equations in some applications. Associated with the symmetry group theory is the study of nonlinear partial differential equations method an effective tool in the field of mathematical physics plays a very important role. Application symmetry method , you can make similar equation reduction, reduction, group classification , structure conservation laws and exact solutions of equations . The traditional symmetrical ( also known as the Lie symmetry ) Act to promote, we got some more general approach , for example: the generalized symmetry method , conditional symmetry method , generalized conditional symmetry methods. Generalized conditional symmetry which solved some with initial value / boundary value nonlinear partial differential equation problem , which is the traditional method difficult to achieve symmetry . The main work is as follows : The first chapter introduces the mathematical mechanization thinking soliton theory of history and development , as well as symmetry method . Outlines the relevant aspects of the domestic and international research and development overview . The second chapter introduces Professor Zhang Hongqing proposed AC = BD theory, introduced the basic content of CD on the theory and ideas . Chapter III study integrable CDGKS equation finite symmetric transformation group and exact solutions . Starting from the Lax pair , the application of the improved direct method , we got CDGKS equation finite symmetric transformation group and exact solutions and further get the corresponding Lie point symmetry. The fourth chapter studies the conditions that allow generalized symmetric quasi-linear evolution equations initial value problem solving . Using the generalized conditional symmetry method has been quasi-linear evolution equations complete group classification and reduction of Cauchy problem , and then get the initial value problem with a quasi-linear evolution equations exact solution . We found a generalized conditional symmetry and AC = BD some relationships between theory .

Related Dissertations

  1. Frobenius nonlinear evolution equations integrable solutions and the expansion of integrable systems,O175.5
  2. Study of Several Types Methods of Construction of the Solutions of the Nonlinear Evolution Equations,O175.29
  3. The Research of Solving the Nonlinear Evolution Equations in Soliton Theory,O175.29
  4. Analysis of the exact solution of the nonlinear equations and solving method,O175.29
  5. Study on Some Nonlinear Evolution Equations in Physics,O175.29
  6. Research on Petrov-Galerkin Spectral Method for Two Problems,O241.82
  7. Fully Discrete Finite Volume Method and Discontinuous Galerkin Finite Element Method for a Class of Nonlinear Evolution Equations,O241.82
  8. A new analytical method of nonlinear evolution equations KS class of equations,O175.29
  9. Study on Exact Solutions for the (2+1) Dimensional Breaking Soliton Equations and WBK Equtions,O175.29
  10. Solving the Nonlinear Evolution Equations and the Darboux Transformation,O175.29
  11. Some Investigation on the New Methods for Finding Exact Solutions of Nonlinear Evolution Equations,O175.29
  12. The Long-time Behavior for A Class of Nonlinear Evolution Equations,O175.29
  13. Several types of exact solutions of partial differential structure,O175.29
  14. Exact solution of some nonlinear systems and conservation laws,O175.29
  15. Solution of nonlinear evolution equations structural problems,O175.29
  16. Traveling Waves and Entire Solutions in a Delayed Diffusive Epidemic Model,O175
  17. Nonlinear evolution equations of conservation laws of certain construction method and its application,O175.2
  18. Generalized conditional symmetries and exact solutions of nonlinear reaction-diffusion equation,O175.2
  19. Exact Solutions and Conservation Laws to Some Nonlinear Evolution Equations,O175.29
  20. Adiabatic Evolution of Coherent State of Trapped and Anti-trapped Single Electron in Low-dimension,O469

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
© 2012 www.DissertationTopic.Net  Mobile