Mathematics of Complexity and Dynamical Systems

2011 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Solitons, Introduction to

  • Mohamed A. Helal
Reference work entry

The concept of solitons reflects one of the most important developments in science at the second half of the 20th century: the nonlinear description of the world. It is not easy to give a comprehensive and precise definition of a soliton. Frequently, a soliton is explained as a spatially localized wave in a medium that can interact strongly with other solitons but will afterwards regain its original form.

It is a nonlinear pulse‐like wave that can exist in some nonlinear systems. The soliton wave can propagate without dispersing its energy over a large region of space; collision of two solitons leads to unchanged forms, solitons also exhibit particle-like properties.

The most remarkable property of solitons is that they do not disperse and thus conserve their form during propagation and collision.  Solitons Interactions.

The nonlinear science has been growing for approximately fifty years. However, numerous nonlinear processes had been previously identified, but the nonlinear...


Solitary Wave Homotopy Analysis Method Vries Equation Homotopy Perturbation Method Variational Iteration Method 
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© Springer-Verlag 2012

Authors and Affiliations

  • Mohamed A. Helal
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt