Symmetry and Exact Solutions of Cylindrically Symmetric Wave

发布时间：2021-08-07 08:02

　　In this work,sets out the conditions conformal invariance cylindrically symmetric nonlinear wave equation D’ Alembert （?） relatively conformal algebra AC（l,n-1）.This eliminated relationship between exponent functions F（x,u）= λun+3/n-1 of number of spatial variables exist for classical equation□u=F（x,u）for requirement of conformal invariance relation algebra AC（l,n）.A search of invariants and ansatzes conformal algebra AC（1,1）,which is used for finding exact solutions of cylindrically-symmetric i... 

【文章来源】：兰州交通大学甘肃省

【文章页数】：53 页

【学位级别】：硕士

【文章目录】：
abstract
Chapter 1 Introduction
    1.1 Motivation
    1.2 Literature review
        1.2.1 History of the question
        1.2.2 Modern approaches
    1.3 Thesis Outline/Organization
Chapter 2 Classical method of symmetric reduction
    2.1 One-parameter transformation groups
        2.1.1 Concept of one-parameter transformation group
        2.1.2 The tangential field of vectors. Equation Lie
        2.1.3 Infinitesimal group operator. Invariants of group
    2.2 Groups,which allow differential equations in partial derivatives
        2.2.1. Continuation methods
        2.2.2. Indicial equationas
Chapter 3 Research of symmetry non-linear wave equation and its use for searching of precise decisions
    3.1. Use symmetry to searching precise decisions cylindrical-symmetric non-linear wave equation
    3.2. The cylindrical-symmetric non-linear wave equation
Chapter 4 Conclusion
Acknowledgements
Reference
Publications



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