This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.
Зміст
Preface to the Second Edition
Preface to the First Edition
Linear Partial Differential Equations
Nonlinear Model Equations and Variational Principles
First-Order, Quasi-Linear Equations and Method of Characteristics
First-Order Nonlinear Equations and Their Applications
Conservation Laws and Shock Waves
Kinematic Waves and Real-World Nonlinear Problems
Nonlinear Dispersive Waves and Whitham’s Equations
Nonlinear Diffusion-Reaction Phenomena
Solitons and the Inverse Scattering Transform
The Nonlinear Schroedinger Equation and Solitary Waves
Nonlinear Klein–Gordon and Sine-Gordon Equations
Asymptotic Methods and Nonlinear Evolution Equations
Tables of Integral Transforms
Answers and Hints to Selected Exercises
Bibliography
Index
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