Nonlinear partial differential equations for scientists and engineers

by Lokenath Debnath

This book presents a comprehensive and systematic treatment of nonlinear partial differential equations and their varied applications. It contains methods and properties of solutions along with their physical significance. In an effort to make the book useful for a diverse readership, 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 is an exceptionally complete and accessible text/reference for graduates and professionals in mathematics, physics, science, and engineering. It is also suitable as a self-study/reference guide.

Genres: Mathematics

593 pages, Hardcover

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.