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

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.