Solitons: Waves with many Attributes of Particles*

Abstract

The purpose of this article is to expose the students and other readers to the wonderful world of solitons – the self-sustaining solitary waves. Beginning with a brief review of the history of their discovery as waves on water surface and their modeling by the Korteweg-de Vries nonlinear partial differential equation, and characterization as particles, we have given a concrete definition for these. A simple soliton solution for the afore-mentioned equation has been elucidated. Also included is a summary of Sine-Gordon and Nonlinear Schro¨dinger equations. The question ‘why care for solitons?’ has been answered by giving an overview of multifaceted theoretical and practical applications of its concepts in various branches of science, particularly physics. Effort has been made to keep the presentation as elementary as possible omitting some mathematical subtleties of the subject.