Soliton Dynamics of a Gauged Fokas-Lenells Equation Under Varying Effects of Dispersion and Nonlinearity

TL;DR

This paper investigates the soliton dynamics of a gauged Fokas-Lenells equation considering varying dispersion and nonlinearity effects, using Hirota's method to derive solutions relevant to optical and plasma systems.

Contribution

It introduces a modified equation incorporating variable dispersion effects and analyzes soliton behavior, expanding understanding of nonlinear wave dynamics under varying conditions.

Findings

Derived soliton solutions using Hirota bilinear method.

Analyzed soliton behavior with respect to dispersion variation.

Applicable to optical pulses, plasma waves, and BEC matter-waves.

Abstract

Davydova-Lashkin-Fokas-Lenells equation (DLFLE) is a gauged equivalent form of Fokas-Lenells equation (FLE) that addresses both spatio-temporal dispersion (STD) and nonlinear dispersion (ND) effects. The balance between those effects results a soliton which has always been an interesting topic in research due to its potential applicability as signal carrier in information technology. We have induced a variation to the dispersion effects and apply Hirota bilinear method to realise soliton solution of the proposed DLFLE and explore how the soliton dynamic behaves in accordance to the variation of the dispersion effects. The proposed equation is applicable for number of systems like ultrashort optical pulse, ioncyclotron plasma wave, Bose-Einstein condensate (BEC) matter-wave soliton under certain external fields, etc. The study on such systems under varying effects is very limited and we hope our work can benefit the researchers to understand soliton dynamics more and work on various other nonlinear fields under varying effects.