Soliton Solutions for Various Nonlinear Models by Sub-ODE Technique

Abstract

Solitons are a special kind of wave or particle-like disturbance that propagates through a medium while maintaining its speed and shape. It has a self-reinforcing waveform that can move over great distances without losing energy or altering its shape. John Scott Russell, a Scottish engineer, first observed a single wave in a restricted canal and noted its pecu- liar behaviour in the 19th century, which is when solitons were first identified. Utilised in optical fibres, solitons allow for high-capacity data transmission by being able to transmit information over long distances without adding any distortion. Here’s a prime illustration. Our study’s main goal is to find several soltons for a nonlinear model of the Biswas-Arshed equation (BAE). By using the sub-ODE approach under constraint conditions, we obtain solutions such as bright, dark, Jacobian elliptic function (JEF), Weierstrass elliptic function (WEF), rational and periodic hyperbolic function. By converting nonlinear partial differ- ential equations (PDEs) into a system of ordinary differential equations (ODEs) based on precise assumptions about the solution’s form, a method known as the sub-ODE method is used to analyse soliton solutions in PDEs. Using basic, solvable ODEs known as sub- ODEs, this strategy has the explicit goal of identifying wave solutions inside a complex model.