Partial Differential Equations and Solitary Waves Theory 1st edition by Abdul Majid Wazwaz 9783642002519 364200251X

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ISBN 10: 364200251X
ISBN 13: 9783642002519 
Author: Abdul-Majid Wazwaz

“Partial Differential Equations and Solitary Waves Theory” is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

Partial Differential Equations and Solitary Waves Theory 1st Table of contents:

Basic Concepts

Firstorder Partial Differential Equations

One Dimensional Heat Flow

Higher Dimensional Heat Flow

One Dimensional Wave Equation 143

Higher Dimensional Wave Equation

Laplaces Equation

Nonlinear Partial Differential Equations

Linear and Nonlinear Physical Models

Numerical Applications and Padé Approximants 415

Solitons and Compactons

The Family of the KdV Equations

KdV and mKdV Equations of Higherorders

Family of KdVtype Equations 605

Boussinesq KleinGordon and Liouville Equations

Burgers Fisher and Related Equations 665

Families of CamassaHolm and Schrodinger Equations

Appendix 699

Exact Solutions of Burgers Equation

E The Error and Gamma Functions

F Infinite Series

Index

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