TY - JOUR
T1 - Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media
AU - Zhong, Ming
AU - Chen, Yong
AU - Yan, Zhenya
AU - Malomed, Boris A.
N1 - Publisher Copyright:
©2024 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2024/1/24
Y1 - 2024/1/24
N2 - We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α1 α2 ∈ (1, 2], and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1, can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too.
AB - We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α1 α2 ∈ (1, 2], and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1, can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too.
KW - modulational instability
KW - numerical methods
KW - rogue-wave excitation
KW - soliton interactions
KW - suppression of soliton collapses
KW - two-Levy-index fractional nonlinear Schrodinger equation
UR - http://www.scopus.com/inward/record.url?scp=85183982451&partnerID=8YFLogxK
U2 - 10.1098/rspa.2023.0765
DO - 10.1098/rspa.2023.0765
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AN - SCOPUS:85183982451
SN - 1364-5021
VL - 480
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2282
M1 - 20230765
ER -