Modulational instability in weak nonlocal nonlinear media with competing Kerr and non-Kerr nonlinearities

Dieudonné Zanga, Serge I. Fewo, Conrad B. Tabi, Timoléon C. Kofané

Research output: Contribution to journalArticle

Abstract

We investigate, theoretically and numerically, the modulational instability of plane waves in weakly cubic-quintic nonlocal nonlinear media. Theoretically, the Lenz transformation and the linear stability analysis are used to study the impact of cubic and quintic nonlocalities on modualtional instability through the stability diagram in different modes of nonlinearity. Moreover, the time-dependent criterion predicting the existence of the modulational instability for any value of the wave number is expressed. In the numerical part, the direct integration of the nonlinear Schrödinger equation, with the split-step method, shows the disintegration dynamics of plane wave in weakly quintic media. Theoretical predictions are in good agreement with numerical results. Particularly, the impact of the cubic and quintic nonlocalities on modulational instability is such that higher values of the quintic nonlocality contribute to reduce the modulational instability in the system. Moreover, the three-body interaction in the model gives rise to Akhmediev breathers, which are the nonlinear manifestation of modulational instability.

Original languageEnglish
Article number104993
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume80
DOIs
Publication statusPublished - Jan 1 2020

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Modulational Instability
Quintic
Nonlocality
Nonlinearity
Plane Wave
Breathers
Linear Stability Analysis
Linear stability analysis
Nonlinear Equations
Disintegration
Diagram
Nonlinear equations
Numerical Results
Prediction
Interaction

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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title = "Modulational instability in weak nonlocal nonlinear media with competing Kerr and non-Kerr nonlinearities",
abstract = "We investigate, theoretically and numerically, the modulational instability of plane waves in weakly cubic-quintic nonlocal nonlinear media. Theoretically, the Lenz transformation and the linear stability analysis are used to study the impact of cubic and quintic nonlocalities on modualtional instability through the stability diagram in different modes of nonlinearity. Moreover, the time-dependent criterion predicting the existence of the modulational instability for any value of the wave number is expressed. In the numerical part, the direct integration of the nonlinear Schr{\"o}dinger equation, with the split-step method, shows the disintegration dynamics of plane wave in weakly quintic media. Theoretical predictions are in good agreement with numerical results. Particularly, the impact of the cubic and quintic nonlocalities on modulational instability is such that higher values of the quintic nonlocality contribute to reduce the modulational instability in the system. Moreover, the three-body interaction in the model gives rise to Akhmediev breathers, which are the nonlinear manifestation of modulational instability.",
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Modulational instability in weak nonlocal nonlinear media with competing Kerr and non-Kerr nonlinearities. / Zanga, Dieudonné; Fewo, Serge I.; Tabi, Conrad B.; Kofané, Timoléon C.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 80, 104993, 01.01.2020.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Modulational instability in weak nonlocal nonlinear media with competing Kerr and non-Kerr nonlinearities

AU - Zanga, Dieudonné

AU - Fewo, Serge I.

AU - Tabi, Conrad B.

AU - Kofané, Timoléon C.

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AB - We investigate, theoretically and numerically, the modulational instability of plane waves in weakly cubic-quintic nonlocal nonlinear media. Theoretically, the Lenz transformation and the linear stability analysis are used to study the impact of cubic and quintic nonlocalities on modualtional instability through the stability diagram in different modes of nonlinearity. Moreover, the time-dependent criterion predicting the existence of the modulational instability for any value of the wave number is expressed. In the numerical part, the direct integration of the nonlinear Schrödinger equation, with the split-step method, shows the disintegration dynamics of plane wave in weakly quintic media. Theoretical predictions are in good agreement with numerical results. Particularly, the impact of the cubic and quintic nonlocalities on modulational instability is such that higher values of the quintic nonlocality contribute to reduce the modulational instability in the system. Moreover, the three-body interaction in the model gives rise to Akhmediev breathers, which are the nonlinear manifestation of modulational instability.

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