Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

T. Uthayakumar, L. Al Sakkaf, U. Al Khawaja

Research output: Contribution to journalReview articlepeer-review

2 Citations (Scopus)

Abstract

This study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems. The historical perspectives include the various analytical techniques developed for constructing the Peregrine soliton solutions, followed by the derivation of the general breather solution of the fundamental nonlinear Schrödinger equation through Darboux transformation. Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.

Original languageEnglish
Article number596886
JournalFrontiers in Physics
Volume8
DOIs
Publication statusPublished - Dec 3 2020

Keywords

  • Peregrine solitons
  • coupled and discrete nonlinear Schrödinger equation
  • higher dimensional nonlinear Schrödinger equation
  • higher order and inhomogeneous nonlinear Schrödinger equation
  • nonlinear Schrödinger equation
  • nonlocal nonlinear Schrödinger equation
  • rogue waves
  • saturable nonlinear Schrödinger equation

ASJC Scopus subject areas

  • Biophysics
  • Materials Science (miscellaneous)
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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