California State University, Northridge WordmarkOviatt Library WordmarkOviatt Library Catalog Wordmark
Author Xu, Xiaoping, author.
Title Algebraic approaches to partial differential equations / Xiaoping Xu.
Published Heidelberg ; New York : Springer, [2013]
Book Cover
 Floor4  QA377 .X8 2013    IN LIBRARY
Description xxiv, 394 pages ; 25 cm
Content Type text
Format volume
Bibliography Includes bibliographical references (pages 385-391) and index.
Contents 1. First-order ordinary differential equations -- 2. Higher order ordinary differential equations -- 3. Special functions -- 4. First-order of linear equations -- 5. Nonlinear scalar equations -- 6. Nonlinear Schrödinger and Davey-Stewartson equations -- 7. Dynamic convection in a sea -- 8. Boussinesq equations in geophyics -- 9. Navier-Stokes equations -- 10. Classical boundary layer problems.
Summary 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 Schrödinger 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.
Subject Differential equations, Partial.
ISBN 3642368735
9783642368745 (ebook)
OCLC number 828494494