Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds

Stanko N. Nikolić*, Omar A. Ashour, Najdan B. Aleksić, Milivoj R. Belić, Siu A. Chin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We investigate the generation of breathers, solitons, and rogue waves of the quintic nonlinear Schrödinger equation (QNLSE) on uniform and elliptical backgrounds. The QNLSE is the general nonlinear Schrödinger equation that includes all terms up to the fifth-order dispersion. We use Darboux transformation to construct initial conditions for the dynamical generation of localized high-intensity optical waves. The condition for the breather-to-soliton conversion is provided with the analysis of soliton intensity profiles. We discover a new class of higher-order solutions in which Jacobi elliptic functions are set as background seed solutions of the QNLSE. We also introduce a method for generating a new class of rogue waves—the periodic rogue waves—based on the matching of the periodicity of higher-order breathers with the periodicity of the background dnoidal wave.

Original languageEnglish
Pages (from-to)2855-2865
Number of pages11
JournalNonlinear Dynamics
Volume95
Issue number4
DOIs
Publication statusPublished - 1 Mar 2019
Externally publishedYes

Keywords

  • Darboux transformation
  • Quintic nonlinear Schrödinger equation
  • Rogue waves

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