ENGLISH

Algebraic Approaches to Partial Differential Equations

By Xiaoping Xu (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2013
ISBN
978-3-642-36873-8, 978-3-642-36874-5
DOI
10.1007/978-3-642-36874-5
Language
english
Format
PDF
Filesize
3 MB (3189718 bytes)
Edition
1
Pages
394\407
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Partial Differential Equations; Mathematical Physi

Description

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.

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