Soliton: A dispersion-less solution with existence and its types

Geeta Arora; Richa Rani; Homan Emadifar

doi:10.1016/j.heliyon.2022.e12122

Soliton: A dispersion-less solution with existence and its types

Heliyon. 2022 Dec 7;8(12):e12122. doi: 10.1016/j.heliyon.2022.e12122. eCollection 2022 Dec.

Authors

Geeta Arora¹, Richa Rani¹, Homan Emadifar²

Affiliations

¹ Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India.
² Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.

Abstract

A solitary wave is the dispersion-less solution of nonlinear evolutionary equations that travels at a constant speed without dissipating its energy. The purpose of this article is to provide insight into the discovery and history of solitons. The different types of the solitons are discussed in brief that is helpful for the researchers. For the discussion of the nature of solitons, the solution behavior of the Korteweg de Vries equation (KdV), the sine-Gordon (SG), the Camassa-Holm (CH) equation, and the nonlinear Schrodinger (NLS) equation are considered. This article deals with the various applications of solitons in different fields such as biophysics, nonlinear optics, Bose-Einstein condensation, plasma physics, Josephson junction, etc. focusing on the properties of solitons based on their classification.

Keywords: Camassa-Holm equation; Korteweg de Vries equation; Nonlinear Schrodinger equation; Properties of solitons; Solitons; sine-Gordon equation.

Publication types

Review