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

• Published in: Communications in nonlinear science & numerical simulation Vol. 80; p. 104993
• Main Authors: Zanga, Dieudonné, Fewo, Serge I., Tabi, Conrad B., Kofané, Timoléon C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2020; Elsevier Science Ltd
• Subjects: Breathers; Disintegration; Modulation instability; Non-kerr nonlinearities; Nonlinear systems; Nonlinearity; Nonlocality; Numerical analysis; Plane waves; Predictions; Schrodinger equation; Stability; Stability analysis; Systems stability; Theoretical mathematics; Time dependence; Waveform analysis; Modulation instability; Nonlocality; Non-kerr nonlinearities
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.104993

•The modulational instability of plane waves, in weakly cubic-quintic nonlocal nonlinear media, is studied.•The impact of cubic and quintic nonlocalities on modualtional instability is addressed•Theoretical predictions are in good agreement with numerical results.•Higher values of the quintic nonlocality reduce the modulational instability.•The three-body interaction in the model gives rise to trains of Akhmediev breathers under modulational instability. 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.