© 2012

Nonlinear Waves and Solitons on Contours and Closed Surfaces

  • Fully revised and updated 2nd edition transparently introduces the theory of nonlinear waves and solitons in the special environment of compact spaces

  • Provides the necessary mathematical framework for treating the manifolds considered with relevant notions from topology and differential geometry

  • Applies the theory to many concrete examples appearing in the physical and related sciences


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

About this book


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.


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

  1. 1., Department of MathematicsEmbry-Riddle Aeronautical UniversityDaytona BeachUSA

Bibliographic information


From the reviews of the second edition:

“This book is devoted to the detailed exposition of the present state of research in the field of nonlinear dynamics of boundaries of physical systems which in the two-dimensional case reduces to the so-called contour dynamics. … The text is intended to be an introduction to the physics and mathematics of solitons on compact systems … . In general, this book can serve as a source of information for students and researchers in nonlinear physics on nonlinear dynamics of compact systems.” (Anatoly M. Kamchatnov, Mathematical Reviews, September, 2013)

“This book is an update of the first edition … and deals with models of nonlinear media filling closed (compact) curves and surfaces. The main subject is a systematic construction and study of solitons states in such systems. … the book may be used as a basis for a graduate course on the theory of nonlinear waves and solitons.” (Boris A. Malomed, Zentralblatt MATH, Vol. 1253, 2013)