This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.

Klappentext

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.

Inhalt

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