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

Fuente: arXiv
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Main Authors: Lashkin, Volodymyr M., Cheremnykh, Oleg K.
Format: Preprint
Published: 2024
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author Lashkin, Volodymyr M.
Cheremnykh, Oleg K.
author_facet Lashkin, Volodymyr M.
Cheremnykh, Oleg K.
contents We study the fractional three-dimensional (3D) nonlinear Schrödinger equation with exponential saturating nonlinearity. In the case of the Lévy 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_05354
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Three-dimensional solitons in fractional nonlinear Schrödinger equation with exponential saturating nonlinearity
Lashkin, Volodymyr M.
Cheremnykh, Oleg K.
Pattern Formation and Solitons
We study the fractional three-dimensional (3D) nonlinear Schrödinger equation with exponential saturating nonlinearity. In the case of the Lévy 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.
title Three-dimensional solitons in fractional nonlinear Schrödinger equation with exponential saturating nonlinearity
topic Pattern Formation and Solitons
url https://arxiv.org/abs/2407.05354