Chirped Embedded Solitons in a Nonlinear Schrödinger Equation with a Saturable Nonlinearity and Fourth-Order Dispersion

Abstract

In this article we study the solitary wave solutions of a generalized nonlinear Schrödinger equation which contains fourth-order dispersion and a saturable nonlinearity. We obtain both: variational solutions and direct numerical solutions. The variational method leads to an averaged Lagrangian, and Euler-Lagrange equations, which contain the dilogarithm (also known as Spence’s function), which is an interesting result from a mathematical point of view, since this special function rarely appears in the description of optical solitons. The variational solutions show that the equation studied has chirped embedded solitons, and these solitons are stable solutions. The direct numerical solutions confirm that the equation under study has chirped standard and embedded solitons, but these pulses transform into chirp-free solitons as the pulses advance along the z direction. The direct numerical solutions also show that the equation studied permits the propagation of breathers.