Dynamical evolutions of optical smooth positons in variable coefficient nonlinear Schrödinger equation with external potentials

Abstract

We construct the optical smooth positon solutions for the generalized variable coefficient nonlinear Schrödinger equation with longitudinally varying dispersion, nonlinearity, linear and harmonic potentials. By employing the similarity transformation technique, we derive this solution along with the homogeneous smooth positon solutions of the basic NLS equation and the integrable requirement. The dynamical properties of the constructed second- and third-order positon solutions are investigated considering the two physical scenarios. In the first situation, we consider a longitudinally variable linear potential while keeping the dispersion parameter constant. In the second scenario, we take into account three different types of modulated dispersion parameters, namely quadratic, exponential, and linear, to analyze the various features in the intensity profile of inhomogeneous optical smooth positons. In both situations, we observe a wide range of significant nonlinear phenomena in the intensity profiles of positons. These phenomena include amplification, deformation, compression, prolongation, suppression, and distortion. Our findings could make a significant contribution to intriguing nonlinear optics experiments focused on investigating optical positons.