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＜電子ブック＞
Algebraic Approaches to Partial Differential Equations / by Xiaoping Xu

版	1st ed. 2013.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2013
本文言語	英語
大きさ	XXIV, 394 p : online resource
著者標目	*Xu, Xiaoping author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics LCSH:Mathematics FREE:Differential Equations FREE:Mathematical Physics FREE:Applications of Mathematics
一般注記	Preface -- Introduction -- Ordinary Differential Equations -- Partial Differential Equations -- Bibliography -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-642-36874-5

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