Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Solitons, Introduction to

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_508-4

The concept of solitons reflects one of the most important developments in science in the second half of the twentieth 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, and 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 50 years. However, numerous nonlinear processes had been previously identified, but the nonlinear...

Keywords

Solitary Wave Homotopy Analysis Method Nonlinear Partial Differential Equation Homotopy Perturbation Method Shallow Water Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsCairo UniversityGizaEgypt