Painlevé analysis of a nonlinear Schrödinger equation discussing dynamics of solitons in optical fiber

Abstract

In this paper, we investigated a new form of nonlinear Schrödinger equation (NLSE), namely the Biswas–Arshed model (BAM) for the analysis of complete integrability with the help of Painlevé test ([Formula: see text]-test). By applying this test, we analyze the singularity structure of the solutions of BAM, knowing the fact that the absence of specific sort of singularities like moveable branch points is a patent signal for the complete integrability of the discussed model. Passing the [Formula: see text]-test is a powerful indicator that the studied model is resolvable by means of inverse scattering transformation (IST).