Ebook: Algebraic Approaches to Partial Differential Equations

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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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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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:
Front Matter....Pages I-XXIV
Front Matter....Pages 1-1
First-Order Ordinary Differential Equations....Pages 3-16
Higher Order Ordinary Differential Equations....Pages 17-35
Special Functions....Pages 37-63
Front Matter....Pages 65-65
First-Order or Linear Equations....Pages 67-140
Nonlinear Scalar Equations....Pages 141-178
Nonlinear Schr?dinger and Davey–Stewartson Equations....Pages 179-211
Dynamic Convection in a Sea....Pages 213-230
Boussinesq Equations in Geophysics....Pages 231-267
Navier–Stokes Equations....Pages 269-316
Classical Boundary Layer Problems....Pages 317-383
Back Matter....Pages 385-394

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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.
Content:
Front Matter....Pages I-XXIV
Front Matter....Pages 1-1
First-Order Ordinary Differential Equations....Pages 3-16
Higher Order Ordinary Differential Equations....Pages 17-35
Special Functions....Pages 37-63
Front Matter....Pages 65-65
First-Order or Linear Equations....Pages 67-140
Nonlinear Scalar Equations....Pages 141-178
Nonlinear Schr?dinger and Davey–Stewartson Equations....Pages 179-211
Dynamic Convection in a Sea....Pages 213-230
Boussinesq Equations in Geophysics....Pages 231-267
Navier–Stokes Equations....Pages 269-316
Classical Boundary Layer Problems....Pages 317-383
Back Matter....Pages 385-394
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