Three-dimensional solitons in fractional nonlinear Schrödinger equation with exponential saturating nonlinearity

Volodymyr M. Lashkin and Oleg K. Cheremnykh

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

Abstract: We study the fractional three-dimensional (3D) nonlinear Schrödinger equation with exponential saturating nonlinearity. In the case of the Levy index α=1.9, this equation can be considered as a model equation to describe strong Langmuir plasma turbulence. The modulation instability of a plane wave is studied, the regions of instability depending on the Lévy index, and the corresponding instability growth rates are determined. Numerical solutions in the form of 3D fundamental soliton (ground state) are obtained for different values of the Lévy index. It was shown that in a certain range of soliton parameters it is stable even in the presence of a sufficiently strong initial random disturbance, and the self-cleaning of the soliton from such initial noise was demonstrated.

Keywords: Fractional nonlinear Schrödinger equation; Three-dimensional soliton; Saturating nonlinearity; Modulational instability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008063

DOI: 10.1016/j.chaos.2024.115254

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