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© 2009

Partial Differential Equations and Solitary Waves Theory

Benefits

  • 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

Book

Part of the Nonlinear Physical Science book series (NPS)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Partial Differential Equations

    1. Front Matter
      Pages 1-1
    2. Abdul-Majid Wazwaz
      Pages 3-17
    3. Abdul-Majid Wazwaz
      Pages 19-68
    4. Abdul-Majid Wazwaz
      Pages 69-106
    5. Abdul-Majid Wazwaz
      Pages 107-141
    6. Abdul-Majid Wazwaz
      Pages 143-194
    7. Abdul-Majid Wazwaz
      Pages 195-236
    8. Abdul-Majid Wazwaz
      Pages 237-284
    9. Abdul-Majid Wazwaz
      Pages 285-351
    10. Abdul-Majid Wazwaz
      Pages 353-413
    11. Abdul-Majid Wazwaz
      Pages 415-455
    12. Abdul-Majid Wazwaz
      Pages 457-475
  3. Solitray Waves Theory

    1. Front Matter
      Pages 477-477
    2. Abdul-Majid Wazwaz
      Pages 479-502
    3. Abdul-Majid Wazwaz
      Pages 503-556
    4. Abdul-Majid Wazwaz
      Pages 557-603
    5. Abdul-Majid Wazwaz
      Pages 605-637
    6. Abdul-Majid Wazwaz
      Pages 639-663
    7. Abdul-Majid Wazwaz
      Pages 665-681

About this book

Introduction

"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.

Keywords

Adomian decomposition HEP NPS PDE Partial Differential Equations Solitary Waves Solitons Variational Iteration partial differential equation wave equation

Authors and affiliations

  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA

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
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy Physics and Astronomy (R0)
  • Hardcover ISBN 978-3-642-00250-2
  • Softcover ISBN 978-3-642-26909-7
  • eBook ISBN 978-3-642-00251-9
  • Series ISSN 1867-8440
  • Series E-ISSN 1867-8459
  • Edition Number 1
  • Number of Pages , 700
  • Number of Illustrations 14 b/w illustrations, 0 illustrations in colour
  • Additional Information Jointly published with Higher Education Press
  • Topics Analysis
    Mathematical and Computational Engineering
    Engineering, general
  • Buy this book on publisher's site
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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)