Abstract
The soliton is an analytic and exact solution to classes of nonlinear evolution equations. It was discovered in 1965 by Zabusky and Kruskal [1], who were experimenting with numerical solution by computer of the Korteweg-de Vries (KdV) equation. This is a nonlinear partial differential equation and had been introduced at the last century to describe wave motion in shallow canals. Zabusky and Kruskal studied it because of its relevance to the significance in theoretical physics, and named “ soliton” to describe the solitary wave solutions of the KdV because of their partical like behaviour. Soon afterwards, Gardner, Greene, Kruskal and Miura (GGKM) [2] discovered the so-called inverse scattering transform (IST) method to find exact general solutions to the KdV equation. Since then the soliton theory has been advancing rapidly and the IST as well as other methods in the theory have become most powerful tools for solving large class of nonlinear evolution equations (NEEs) including some of physically interesting ones, (usually, the NEEs possessing soliton solutions are called soliton equations). Some other related topics have also been arised, which cover many areas in both mathematics and physics.
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