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Algebraic Approaches to Partial Differential Equations [electronic resource] / by Xiaoping Xu.

By: Xu, Xiaoping [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013Description: XXIV, 394 p. 2 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642368745.Subject(s): Mathematics | Differential equations, partial | Mathematics | Partial Differential Equations | Mathematical Physics | Applications of MathematicsDDC classification: 515.353 Online resources: Click here to access online
Contents:
Preface -- Introduction -- Ordinary Differential Equations -- Partial Differential Equations -- Bibliography -- Index.
In: Springer eBooksSummary: 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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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.

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