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Nonlinear Waves and Solitons on Contours and Closed Surfaces

  • Andrei┬áLudu

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Mathematical Prerequisites

    1. Front Matter
      Pages 1-1
    2. Andrei Ludu
      Pages 3-8
    3. Andrei Ludu
      Pages 9-22
    4. Andrei Ludu
      Pages 23-29
    5. Andrei Ludu
      Pages 79-95
    6. Andrei Ludu
      Pages 97-130
    7. Andrei Ludu
      Pages 131-158
    8. Andrei Ludu
      Pages 159-176
  3. Solitons and Nonlinear Waves on Closed Curves and Surfaces

    1. Front Matter
      Pages 177-178
    2. Andrei Ludu
      Pages 179-221
    3. Andrei Ludu
      Pages 223-257
    4. Andrei Ludu
      Pages 259-288
    5. Andrei Ludu
      Pages 289-308
    6. Andrei Ludu
      Pages 373-381
  4. Physical Nonlinear Systems at Different Scales

    1. Front Matter
      Pages 383-383
    2. Andrei Ludu
      Pages 385-410
    3. Andrei Ludu
      Pages 467-474
  5. Back Matter
    Pages 475-489

About this book

Introduction

This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems.

The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given.

The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics.

This book is intended for graduate students and researchers in mathematics, physics and engineering.

This new edition has been thoroughly revised, expanded and updated.

Keywords

closed curves and surfaces compact boundaries and surfaces contour dynamics introduction soliton theory modeling of solitons nonlinear waves introduced physics of solitons surface waves

Authors and affiliations

  • Andrei┬áLudu
    • 1
  1. 1., Department of MathematicsEmbry-Riddle Aeronautical UniversityDaytona BeachUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22895-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-22894-0
  • Online ISBN 978-3-642-22895-7
  • Series Print ISSN 0172-7389
  • Buy this book on publisher's site
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