Algebraic Approaches to Partial Differential Equations

  • Xiaoping Xu

Table of contents

  1. Front Matter
    Pages I-XXIV
  2. Ordinary Differential Equations

    1. Front Matter
      Pages 1-1
    2. Xiaoping Xu
      Pages 37-63
  3. Partial Differential Equations

    1. Front Matter
      Pages 65-65
    2. Xiaoping Xu
      Pages 67-140
    3. Xiaoping Xu
      Pages 141-178
    4. Xiaoping Xu
      Pages 213-230
    5. Xiaoping Xu
      Pages 231-267
    6. Xiaoping Xu
      Pages 269-316
    7. Xiaoping Xu
      Pages 317-383
  4. Back Matter
    Pages 385-394

About this book

Introduction

This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation,  the KP equation,  the nonlinear Schrodinger equation,  the Davey and Stewartson equations, the Boussinesq equations in geophysics,  the Navier-Stokes equations and the boundary layer problems.  In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions,  symmetry transformations,  linearization techniques  and  special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

Keywords

Algebraic method Asymmetric approach Exact solution Moving frame Partial differential equation Symmetry transformation

Authors and affiliations

  • Xiaoping Xu
    • 1
  1. 1., Institute of MathematicsAcademy of Mathematics and System SciencBeijingChina, People's Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-36874-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-36873-8
  • Online ISBN 978-3-642-36874-5
  • About this book