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

Cihan Bayındır*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

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 Schrödinger 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.

Original languageEnglish
Article number102362
JournalResults in Physics
Volume14
DOIs
Publication statusPublished - Sept 2019

Bibliographical note

Publisher Copyright:
© 2019 The Author

Keywords

  • Kundu-Eckhaus equation
  • Nonlinear optics
  • Spectral renormalization method

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