A SPECTRAL METHOD TO OBTAIN SOLITON SOLUTIONS TO CQNLS EQUATION

Abstract

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

Keywords

• Nonlinear Schrödinger equation,soliton,spectral methods

References

1. Ablowitz, M. J., & Musslimani, Z. H. (2005). Spectral renormalization method for computing self-localized solutions to nonlinear systems. Optics Letters, 30, 2140-2142. Göksel, İ. (2017). Lattice solitons in cubic-quintic media. Ph.D. thesis, İTÜ, Istanbul, Turkey. Göksel, İ., Antar, N., & Bakırtaş, İ. (2015). Solitons of (1+1)D cubic-quintic nonlinear Schrödinger equation with PT-symmetric potentials. Optics Communications, 354, 277-285. doi: 10.1016/j.optcom.2015.05.051 Yang, J. (2010). Nonlinear Waves in Integrable and Nonintegrable Systems. Philadelphia, PA: SIAM.