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Mathematics - Dynamical Systems & Differential Equations | Algebraic Approaches to Partial Differential Equations

Algebraic Approaches to Partial Differential Equations

Xu, Xiaoping

2013, XXIV, 394 p. 2 illus.

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  • Fundamental algebraic techniques of solving PDEs
  • Exact solutions to physical equations
  • Accessibility to general audience
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.

Content Level » Research

Keywords » Algebraic method - Asymmetric approach - Exact solution - Moving frame - Partial differential equation - Symmetry transformation

Related subjects » Applications - Dynamical Systems & Differential Equations

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