Overview
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, \xa0the KP equation, \xa0the nonlinear Schrodinger equation, \xa0the Davey and Stewartson equations, the Boussinesq equations in geophysics, \xa0the Navier-Stokes equations and the boundary layer problems. \xa0In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, \xa0symmetry transformations, \xa0linearization techniques \xa0and \xa0special 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.