Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity

Abstract

We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities.

A Numerical Method for Pulse Propagation in Nonlinear Dispersive Optical Media

“…5 we consider two solitons hyperbolic secant used in the collision models and is written: g(t) = A0sech(t − t1) + rsech(t + t2) exp(iθ); where r is the relative amplitude of the two solitons, θ is the relative phase between them. The parameters are: r = 1, θ = 0 (equal amplitude and in phase case) and t1 = t2 = 2 (initial spacing) [8].…”

“…Let's introduce γ = β0n2LD and N 2 = β0n2I0LD [6], I0 is maximum pulse intensity and N governs the soliton order; LD is the dispersion length. As pointed out in [8], intrapulse Raman scattering is ignored in this work.…”

“…Theoretical and experimental research for the propagation process of ultrashort laser pulses in a medium have been the subject of intensive research within the last few years [1][2][3][4][5][6][7][8]. Wave propagation in an optical fiber is governed by the nonlinear Schr ödinger equation (NLSE).…”