Algebraic Approaches to Partial Differential Equations, 1st Edition

  • Published By:
  • ISBN-10: 3642368743
  • ISBN-13: 9783642368745
  • DDC: 518.64
  • Grade Level Range: College Freshman - College Senior
  • 394 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Ordinary Differential Equations.
2: First-Order Ordinary Differential Equations.
3: Higher Order Ordinary Differential Equations.
4: Special Functions.
5: Partial Differential Equations.
6: First-Order or Linear Equations.
7: Nonlinear Scalar Equations.
8: Nonlinear Schrödinger and Davey-Stewartson Equations.
9: Dynamic Convection in a Sea.
10: Boussinesq Equations in Geophysics.
11: Navier-Stokes Equations.
12: Classical Boundary Layer Problems.