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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.
List of contents
Preface.- Introduction.- Ordinary Differential Equations.- Partial Differential Equations.- Bibliography.- Index.
About the author
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.
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 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.
Additional text
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)
Report
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)
