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

Abstract EN

Using the well-known solitary wave ansatz method, we obtain new exact bright and dark soliton solutions for two nonlinear Schro¨ dinger equations, namely, the perturbed nonlinear Schro¨ dinger equation with the Kerr law nonlinearity and a higher order nonlinear Schro¨ dinger 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.