Analytic combined bright-dark, bright and dark solitons solutions of generalized nonlinear Schrödinger equation using extended Sinh-Gordon equation expansion method

Abstract

In this paper, we find analytic solutions of generalized nonlinear Schrödinger equation (GNLSE), the underlying equation for studying pulse propagation through optical waveguides, by implementing the extended Sinh-Gordon equation expansion method (ShGEEM). Here, the terms corresponding to second and third order dispersion, waveguide’s loss, Kerr Effect, self-steepening and Raman Effect are included in GNLSE. The obtained analytic solutions represent bright, dark and combined bright-dark solitons. The constraint conditions for the existence of valid solutions are given. Also, the new solutions are graphically shown for pulse propagation along a photonic crystal fiber.