Nonlinear Partial Differential Equations for Scientists and Engineers

by Lokenath Debnath

Overview

The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated 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, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.

Product Details

ISBN-13:	9780817682651
Publisher:	Birkhäuser Boston
Publication date:	10/06/2011
Sold by:	Barnes & Noble
Format:	eBook
File size:	20 MB
Note:	This product may take a few minutes to download.

About the Author

Lokenath Debnath is author or co-author of seven graduate-level books and research monographs, including "Introduction to Hilbert Spaces with Applications," "Nonlinear Water Waves," and "Continuum Mechanics" published by Academic Press; "Nonlinear Partial Differential Equations for Scientists and Engineers" and "Wavelets Transforms and Their Applications," published by Birkhauser Boston; "Partial Differential Equations for Scientists and Engineers" published by Prentice Hall; and "Integral Transforms and Their Applications" by CRC Press/Chapman and Hall. He has also edited seven research monographs including "Nonlinear Waves" published by Cambridge University Press and "Wavelet Transforms and Time-Frequency Signal Analysis" published by Birkhauser Boston. He is an author and co-author of over 300 research papers in pure and applied mathematics, encompassing applied partial differential equations, integral transforms and special functions, inequalities, solid and fluid mechanics, linear and nonlinear waves, solitons, magnetohydrodynamics, unsteady boundary layers, dynamics of oceans, wavelet transforms, signal processing, and stability theory.

Table of Contents

Preface to the Third Edition.- Preface.- 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 Schroedinger Equation and Solitary Waves.- Nonlinear Klein—Gordon and Sine-Gordon Equations.- Asymptotic Methods and Nonlinear Evolution Equations.- Tables of Integral Transforms.- Answers and Hints to Selected Exercises.- Bibliography.- Index.

Editorial Reviews

Presents a comprehensive and systematic treatment of nonlinear partial differential equations and their varied applications. Discusses derivation and methods of solutions for all fundamental nonlinear model equations, among them, Korteweg-de Vries, Boussinesq, Burgers, Fisher, and Whitham equations. Covers conservation laws, weak solutions, and shock waves; nonlinear real-world models that include traffic flow, flood waves, chromatographic models, sediment transport in rivers, glacier flow, and roll waves; and solitons and the inverse scattering transform. Gives special emphasis to nonlinear instability of dispersive waves with applications to water waves. Annotation c. by Book News, Inc., Portland, Or.

Booknews

From the reviews:

"An exceptionally complete overview of the latest developments in the field of PDEs. 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."—Applied Mechanics Review (Review of First Edition)

From the reviews of the third edition:

"Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library."—UK Nonlinear News (Review of Second Edition)

“This book provides an introduction to nonlinear partial differential equations that arise throughout in science and engineering and to the basic methods for finding the solutions for these equations. The book contains thirteen chapters and three appendixes. At the end of the first twelve chapters there are exercises that help to understand the subject matter. … This book is recommended for graduate students in science and engineering.” (Valery V. Karachik, Zentralblatt MATH, Vol. 1242, 2012)

From the Publisher