Overview
- Handles solitary waves theory in an accessible manner
- Combines in two parts an easy-to-read introduction with recent research achievements
- Graphs of all types of travelling waves illustrate the basic features of soliton theory
Part of the book series: Nonlinear Physical Science (NPS)
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Table of contents (18 chapters)
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Front Matter
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Partial Differential Equations
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Front Matter
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Keywords
About this book
"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.
Reviews
From the reviews:
“This book is devoted to the study of classical and new methods for solving partial differential equations (linear and nonlinear). … It can be read by undergraduate and graduate students. … will be also very useful for researchers in applied mathematics and engineering because it suggests new and powerful techniques avoiding discretization and linearization I warmly recommend this reference book for its simplicity and its rigour.” (Yves Cherruault, Zentralblatt MATH, Vol. 1175, 2010)Authors and Affiliations
Bibliographic Information
Book Title: Partial Differential Equations and Solitary Waves Theory
Authors: Abdul-Majid Wazwaz
Series Title: Nonlinear Physical Science
DOI: https://doi.org/10.1007/978-3-642-00251-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Hardcover ISBN: 978-3-642-00250-2Published: 13 August 2009
eBook ISBN: 978-3-642-00251-9Published: 28 May 2010
Series ISSN: 1867-8440
Series E-ISSN: 1867-8459
Edition Number: 1
Number of Pages: 700
Number of Illustrations: 14 b/w illustrations
Additional Information: Jointly published with Higher Education Press
Topics: Analysis, Mathematical and Computational Engineering, Engineering, general