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Partial Differential Equations and Solitary Waves Theory

  • Abdul-Majid Wazwaz

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
    8. Abdul-Majid Wazwaz
      Pages 683-697
  4. Back Matter
    Pages 699-742

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

  • Abdul-Majid Wazwaz
    • 1
  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA

Bibliographic information

  • 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
  • Print ISBN 978-3-642-00250-2
  • Online ISBN 978-3-642-00251-9
  • Series Print ISSN 1867-8440
  • Buy this book on publisher's site