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Nonlinear Partial Differential Equations for Scientists and Engineers
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Nonlinear Partial Differential Equations for Scientists and Engineers

Nonlinear Partial Differential Equations for Scientists and Engineers

Lokenath Debnath

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

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
Voir tout
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Lokenath Debnath
Parution 01/06/2004
Édition  2eme 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

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