The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation.
Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.
Author(s): Lokenath Debnath (auth.)
Edition: 3
Publisher: Birkhäuser Basel
Year: 2012
Language: English
Pages: 860
Tags: Partial Differential Equations;Applications of Mathematics;Theoretical, Mathematical and Computational Physics;Mathematical Methods in Physics;Classical Continuum Physics;Appl.Mathematics/Computational Methods of Engineering
Front Matter....Pages I-XXIII
Linear Partial Differential Equations....Pages 1-147
Nonlinear Model Equations and Variational Principles....Pages 149-199
First-Order, Quasi-linear Equations and Method of Characteristics....Pages 201-226
First-Order Nonlinear Equations and Their Applications....Pages 227-256
Conservation Laws and Shock Waves....Pages 257-281
Kinematic Waves and Real-World Nonlinear Problems....Pages 283-354
Nonlinear Dispersive Waves and Whitham’s Equations....Pages 355-379
Nonlinear Diffusion–Reaction Phenomena....Pages 381-423
Solitons and the Inverse Scattering Transform....Pages 425-533
The Nonlinear Schrödinger Equation and Solitary Waves....Pages 535-577
Nonlinear Klein–Gordon and Sine-Gordon Equations....Pages 579-622
Asymptotic Methods and Nonlinear Evolution Equations....Pages 623-674
Tables of Integral Transforms....Pages 675-687
Back Matter....Pages 689-860
