A SPECTRAL METHOD TO OBTAIN SOLITON SOLUTIONS TO CQNLS EQUATION

Year 2017, Issue: 1, 304 - 309, 09.11.2017

Izzet Goksel Ilkay Bakirtas

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

• 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.