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Algebraic Approaches to Partial Differential Equations (Hardcover, 2013 ed.)
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Algebraic Approaches to Partial Differential Equations (Hardcover, 2013 ed.)
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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.
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