The solitary wave ansatz method for finding the exact bright and dark soliton solutions of two nonlinear Schrödinger equations

Abstract

Using the well-known solitary wave ansatz method, we obtain new exact bright and dark soliton solutions for two nonlinear Schrödinger equations, namely, the perturbed nonlinear Schrödinger equation with the Kerr law nonlinearity and a higher order nonlinear Schrödinger equation which describe the propagation of ultra short pulses in nonlinear optical fibers. The parameters of the soliton envelope (amplitude, width, velocity) are obtained as a function of the dependent model coefficients. Comparing the new solutions for these two equations with the well-known results are given.