Nonlinear Partial Differential Equations for Scientists and Engineers (eBook) von Lokenath Debnath

Preface to the Second EditionPreface to the First EditionLinear Partial Differential EquationsNonlinear Model Equations and Variational PrinciplesFirst-Order, Quasi-Linear Equations and Method of CharacteristicsFirst-Order Nonlinear Equations and Their ApplicationsConservation Laws and Shock WavesKinematic Waves and Real-World Nonlinear ProblemsNonlinear Dispersive Waves and Whitham's EquationsNonlinear Diffusion-Reaction PhenomenaSolitons and the Inverse Scattering TransformThe Nonlinear Schroedinger Equation and Solitary WavesNonlinear Klein--Gordon and Sine-Gordon EquationsAsymptotic Methods and Nonlinear Evolution EquationsTables of Integral TransformsAnswers and Hints to Selected ExercisesBibliographyIndex

'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.