Nonlinear Partial Differential Equations for Scientists and Engineers

Lokenath Debnath

738 pages, parution le 01/06/2004 (2^eme édition)

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Résumé

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 Schrodinger, and Whitham 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.

Sommaire

Preface to the Second Edition
Preface to the First Edition
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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Lokenath Debnath
Parution	01/06/2004
Édition	2^eme édition
Nb. de pages	738
Format	16 x 24
Couverture	Relié
Poids	1180g
Intérieur	Noir et Blanc
EAN13	9780817643232
ISBN13	978-0-8176-4323-2