TY - JOUR
T1 - Solitons in a coupled system of fractional nonlinear Schrödinger equations
AU - Zeng, Liangwei
AU - Belić, Milivoj R.
AU - Mihalache, Dumitru
AU - Li, Jiawei
AU - Xiang, Dan
AU - Zeng, Xuanke
AU - Zhu, Xing
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/12/15
Y1 - 2023/12/15
N2 - Interest in physical systems with fractional derivatives has exploded in the 21st century. Similarly, interest in the localized excitations of nonlinear dynamical systems continues to grow significantly in recent times. In this work, we demonstrate the existence of localized solutions in the nonlinear system of three coupled Schrodinger equations with fractional dispersion, linear coupling, and cubic nonlinearities. We then check the stability of these localized solutions, i.e., solitons, by utilizing the linear stability analysis method and by propagating the perturbed solutions using the split-step fast-Fourier beam propagation method. We also prove that the solitary solutions can be stabilized in this system, thanks to the confining influence of the cross-phase modulation effect. The system is set with the same cross-phase modulation parameter but different self-phase modulation coefficients. We further find that the Levy index (LI), the propagation constant, and the cross-phase modulation effect markedly affect the profiles and the stability domains of the solitons in the three-coupled system. Furthermore, the amplitude of the component with the strongest self-phase modulation is the largest among the three components, and the variation of the LI, the propagation constant, or the cross-phase modulation coefficient does not affect much this result. Besides the common perturbed propagation, the propagation with modulated LI is also investigated in this work, displaying increased instability when the LI is modulated suddenly, as opposed to stable propagation when the change in the LI is gradual.
AB - Interest in physical systems with fractional derivatives has exploded in the 21st century. Similarly, interest in the localized excitations of nonlinear dynamical systems continues to grow significantly in recent times. In this work, we demonstrate the existence of localized solutions in the nonlinear system of three coupled Schrodinger equations with fractional dispersion, linear coupling, and cubic nonlinearities. We then check the stability of these localized solutions, i.e., solitons, by utilizing the linear stability analysis method and by propagating the perturbed solutions using the split-step fast-Fourier beam propagation method. We also prove that the solitary solutions can be stabilized in this system, thanks to the confining influence of the cross-phase modulation effect. The system is set with the same cross-phase modulation parameter but different self-phase modulation coefficients. We further find that the Levy index (LI), the propagation constant, and the cross-phase modulation effect markedly affect the profiles and the stability domains of the solitons in the three-coupled system. Furthermore, the amplitude of the component with the strongest self-phase modulation is the largest among the three components, and the variation of the LI, the propagation constant, or the cross-phase modulation coefficient does not affect much this result. Besides the common perturbed propagation, the propagation with modulated LI is also investigated in this work, displaying increased instability when the LI is modulated suddenly, as opposed to stable propagation when the change in the LI is gradual.
KW - Coupled Schrodinger equations
KW - Cross-phase modulation
KW - Fractional dispersion
KW - Nonlinear optics
KW - Optical solitons
UR - http://www.scopus.com/inward/record.url?scp=85173188973&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2023.133924
DO - 10.1016/j.physd.2023.133924
M3 - Article
AN - SCOPUS:85173188973
SN - 0167-2789
VL - 456
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
M1 - 133924
ER -