Dynamics of optical solitons in the fifth-order nonlinear Schrödinger equation

Abstract

The dynamics of optical solitons in the fifth-order equation of nonlinear Schrödinger type is investigated by Riemann–Hilbert formulation and asymptotic analysis. Firstly, the inverse scattering transform of the fifth-order equation of nonlinear Schrödinger type is developed and the corresponding Riemann–Hilbert problem is established. Then the N-soliton solution is derived by analyzing the Riemann–Hilbert problem in term of discrete spectrums. Finally, the dynamical behaviors of the exact single-soliton, second-order soliton and third-order soliton solutions are analyzed graphically and it is proved that two-soliton solution will be decomposed into two one-soliton solution as time tends to infinity.