Lorentzian Solitary Wave in a Generalised Nonlinear Schr\"odinger Equation

TL;DR

This paper derives a Lorentzian solitary wave solution in a generalized nonlinear Schrödinger equation with an additional nonlinear term, revealing new wave behaviors in such systems.

Contribution

It introduces a new traveling-wave solution with Lorentzian profile for a generalized nonlinear Schrödinger equation including a nonlinear term of the form λψ^q.

Findings

Energy density exhibits Lorentzian solitary wave behavior

Solution extends understanding of wave dynamics in nonlinear Schrödinger equations

Potential applications in nonlinear wave physics

Abstract

We obtain a travelling-wave solution of a generalised nonlinear Schr\"odinger equation with an additional term of the form $\Gamma(\psi(x,t)) = \lambda \psi(x,t)^q$, where $\lambda$ and $q$ are real constants. Moreover, we show that the density of energy of the system for the travelling-wave solution presents a Lorentzian solitary wave behaviour.