A SPECTRAL METHOD TO OBTAIN SOLITON SOLUTIONS TO CQNLS EQUATION

Abstract

In optics, the cubic-quintic nonlinearSchrödinger (CQNLS) equation models electromagnetic wave propagation in variousoptical media. Competing cubic and quintic nonlinearities will allow theexistence of stable soliton solutions (see Göksel et al. (2015)). In this study, a numerical method isintroduced to obtain these solitons in different self-focusing /self-defocusing cubic-quintic media. Solitons obtained numerically by thisspectral method are then validated by comparison with exact solutions.