Self-localized solutions of the Kundu-Eckhaus equation in nonlinear waveguides


Bayındır C.

RESULTS IN PHYSICS, vol.14, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14
  • Publication Date: 2019
  • Doi Number: 10.1016/j.rinp.2019.102362
  • Title of Journal : RESULTS IN PHYSICS

Abstract

In this paper we numerically analyze the 1D self-localized solutions of the Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral renormalization method (SRM) and compare our findings with those solutions of the nonlinear Schrodinger equation (NLSE). For cubic-quintic nonlinearity with Raman effect, as a benchmark problem we numerically construct single, dual and N-soliton solutions for the zero optical potential, i.e. V = 0, which are analytically derived before. We show that self-localized soliton solutions of the KEE with cubic-quintic nonlinearity and Raman effect do exist, at least for a range of parameters, for the photorefractive lattices with optical potentials in the form of V = IoCOS2 (x). Additionally, we also show that self-localized soliton solutions of the KEE with saturable cubic-quintic nonlinearity and Raman effect do also exist for some range of parameters. However, for all of the cases considered, these self-localized solitons are found to be unstable. We compare our findings for the KEE with their NLSE analogs and discuss our results.