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 Schrödinger Equation and Solitary Waves -- Nonlinear Klein-Gordon and Sine-Gordon Equations -- Asymptotic Methods and Nonlinear Evolution Equations -- Tables of Integral Transforms.

"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 (Review of First Edition) 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 areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making 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 Klein--Gordon, sine-Gordon, nonlinear Schrödinger, Euler, Water Waves, Camassa and Holm, Johnson, Davey-Stewartson, Kolmogorov, Petrovsky and Piscunov, Kadomtsev and Petviashivilli, Benjamin, Bona and Mahony, Harry Dym, Lax, and Whitman equations * Systematic presentation and explanation of conservation laws, weak solutions, and shock waves * Solitons, compactons, intrinsic localized modes, and the Inverse Scattering Transform * Special emphasis on nonlinear instability of dispersive waves with applications to water waves * Over 600 worked examples and end-of-chapter exercises with hints and selected solutions New features of the Second Edition include: * Improved presentation of results, methods of solutions, and proofs * New section on Sturm--Liouville systems and their fundamental properties * Revised examples, exercises, and updated applications and references * Several revised, nonlinear real-world models, including traffic flow, flood waves, chromatographic models, sediment transport in rivers, glacier flow, and roll waves Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition is an exceptionally complete and accessible text/reference for graduate students, researchers, and professionals in mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference.