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Solitons in nonintegrable systems.

Roger H J Grimshaw1, Lev A Ostrovsky, Dmitry E Pelinovsky

  • 1Department of Mathematical Sciences, Loughborough University, Loughborough, Leics. LE11 3TU, United Kingdom.

Chaos (Woodbury, N.Y.)
|October 29, 2005
PubMed
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This special focus issue explores solitons in nonintegrable systems, detailing recent advancements. It covers modulation, dynamical evolution, and the stability of solitary waves and embedded solitons.

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Soliton theory

Background:

  • Solitons are fundamental in integrable systems.
  • Understanding solitons in nonintegrable systems presents significant challenges.
  • Recent advancements have spurred new research directions.

Purpose of the Study:

  • To present a collection of recent research on solitons in nonintegrable systems.
  • To provide an overview of current developments and key topics in the field.
  • To consolidate diverse contributions on soliton dynamics and stability.

Main Methods:

  • Review of recent theoretical and computational studies.
  • Analysis of experimental findings related to soliton behavior.
  • Synthesis of contributions covering modulation, evolution, and stability.

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Main Results:

  • Highlights include the modulation of solitons, bores, and shocks.
  • Discusses the complex dynamical evolution of solitary waves.
  • Examines the existence and stability of solitary waves and embedded solitons.

Conclusions:

  • The issue consolidates current knowledge on solitons in nonintegrable systems.
  • It identifies key areas of active research and future directions.
  • Emphasizes the growing importance of studying these phenomena in complex environments.