Algebraic Approaches to Partial Differential Equations

Authors: Xu, Xiaoping

  • Fundamental algebraic techniques of solving PDEs
  • Exact solutions to physical equations
  • Accessibility to general audience
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About this book

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.

About the authors

The author received his Ph.D. from Rutgers University, USA in 1992. He is currently a research professor at the Chinese Academy of Sciences’ Institute of Mathematics, and  has been working on representation theory and applied partial differential equations for twenty years, during which he has published over fifty substantial research papers and two monographs on mathematics.

Reviews

From the book reviews:

“Professor Xu’s treatise is an interesting addition to the literature on exact/explicit solutions to nonlinear partial differential equations. … the present book will be useful for a large audience of applied mathematicians, specialists in numerical analysis, physicists and engineers.” (Enrique G. Reyes, Mathematical Reviews, August, 2014)

Table of contents (10 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-36874-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-36873-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover n/a
  • ISBN 978-3-642-42762-6
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Approaches to Partial Differential Equations
Authors
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-36874-5
DOI
10.1007/978-3-642-36874-5
Hardcover ISBN
978-3-642-36873-8
Softcover ISBN
978-3-642-42762-6
Edition Number
1
Number of Pages
XXIV, 394
Topics