An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here.this reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel."-Applied Mechanics Review
This expanded and enlarged second edition presents 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 areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions, along with their physical significance, help to make the book more useful for a diverse readership.
Topics and Key Features: * Thorough coverage of derivation and methods of solutions for all fundamental nonlinear model equations which include Korteweg-de Vries, Boussinesq, Burgers, Fisher, nonlinear reaction-diffusion, Euler-Lagrange, nonlinear Kleine-Gordon, sine-Gordon, nonlinear Schrödinger, and Whitman equations * Systematic presentation and explanation of conservation laws, weak solutions, and shock waves * Solitions and the Inverse Scattering Transform * Special emphasis on nonlinear instability of dispersive waves with applications to water waves * Over 500 worked examples and end-of-chapter exercises with hints and answers to selected exercises
New features of the Second Edition include: * Improved presentations of results, methods of solutions and proofs * New section on Sturm-Liouville Systems and their fundamental properties * Revised examples, exercises, and updated applications * Several revised nonlinear real-world models that include traffic flow, flood waves, chromatographic models, sediment transport in rivers, glacier flow, and roll waves * Completely updated list of references
Nonlinear Partial Differential Equations for Scientists and Engineers is an exceptionally complete and accessible text/reference for graduate students, researchers, and professionals in mathematics, physics, and engineering. It can be used in graduate-level courses or as a self-study resource.