Effect of third-order dispersion on the solitonic solutions of the schrödinger equations with cubic nonlinearity

H. Chachou Samet, M. Benarous, M. Asad-Uz-Zaman, U. Al Khawaja

Research output: Contribution to journalReview articlepeer-review

2 Citations (Scopus)

Abstract

We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities.

Original languageEnglish
Article number323591
JournalAdvances in Mathematical Physics
Volume2014
DOIs
Publication statusPublished - 2014

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Applied Mathematics

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