Solitary wave solution for inhomogeneous nonlinear Schrödinger system with loss/gain

This paper deals with the propagation of solitons in real fibres, governed by the system of inhomogeneous nonlinear Schrödinger (INLS) equations. The Painlevé singularity structure analysis is utilized to check for the integrability of the system and from the analysis, the system is found to admit soliton-type lossless wave propagation. The system is transformed to its homogeneous counterpart using a suitable variable transformation and the soliton solutions are obtained through Bäcklund transformation after constructing the explicit Lax pair for the system. The one-soliton solutions are plotted for different choices of inhomogeneity parameters and the evolutionary characteristics of the solutions are analyzed.