Nonlinear Partial Differential Equations for Scientists and Engineers

by Lokenath Debnath

1. Linear Partial Differential Equations.- 2. Nonlinear Model Equations and Variational Principles.- 3. First-Order, Quasi-Linear Equations and The Method of Characteristics.- 4. First-Order Nonlinear Equations and Their Applications.- 5. Conservation Laws and Shock Waves.- 6. Kinematic Waves and Specific Real-World Nonlinear Problems.- 7. Nonlinear Dispersive Waves and Whitham's Equations.- 8. Nonlinear Diffusion-Reaction Phenomena, Burgers' and Fisher's Equations.- 9. Solitons and The Inverse Scattering Transform.- 10. The Nonlinear Schrödinger Equation and Solitary Waves.- 11. Nonlinear Klein-Gordon and Sine-Gordon Equations.- 12. Asymptotic Methods and Nonlinear Evolution Equations.- Answers and Hints to Selected Exercises.

Genres: Mathematics

612 pages, Paperback

First published August 19, 1997

Reviews

[Tomáš Ševček · Rating 5 out of 5]

A very informative textbook on (primarily non-linear) PDEs. The book covers a wide range of topics such as variational principles, characteristics, conservation laws, shock waves, dispersive waves, reaction-diffusion equations, solitons, inverse scattering transform, asymptotic methods and others (many of which cannot be found either in such a detail or altogether in Evans). While the topics are advanced, the exposition is quite simple (considering how advanced the topics are) and definitely less formal/rigorous than in Evans, with the focus on the analysis of concrete PDEs/problems rather than on general theorems and proofs. Not much functional analysis is required (not even in the parts on variational principles; real analysis/basic concepts from functional analysis will generally suffice). I recommend the book to anyone who is interested in advanced PDE techniques and their direct applications to a vast range of (natural) real-world phenomena.