Formation and propagation of fundamental and vortex soliton families in 1D and 2D dual-Lévy-index fractional nonlinear Schrödinger equations with cubic-quintic nonlinearity
DOI10.1016/j.physd.2024.134157zbMATH Open1546.35222MaRDI QIDQ6554914
Yong Chen, Zhenya Yan, Ming Zhong, Boris A. Malomed
Publication date: 13 June 2024
Published in: Physica D (Search for Journal in Brave)
variational approximationcubic-quintic nonlinearitysplitting instability1D and 2D dual-Lévy-index fractional nonlinear Schrödinger equationsanisotropic fractionality
Stability in context of PDEs (35B35) Variational methods applied to PDEs (35A15) Fractional derivatives and integrals (26A33) Diffraction, scattering (78A45) NLS equations (nonlinear Schrödinger equations) (35Q55) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60) Perturbations in context of PDEs (35B20) Soliton solutions (35C08) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- The nonlinear Schrödinger equation. Singular solutions and optical collapse
- Symmetric and asymmetric solitons and vortices in linearly coupled two-dimensional waveguides with the cubic-quintic nonlinearity
- Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity
- Chaos, fractional kinetics, and anomalous transport
- Spectrally stable encapsulated vortices for nonlinear Schrödinger equations
- Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium
- Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity
- Soliton dynamics in a fractional complex Ginzburg-Landau model
- Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential
- Quadratic fractional solitons
- L'intégrale de Riemann-Liouville et le problème de Cauchy
- Multidimensional dissipative solitons and solitary vortices
- Revisiting the $\mathcal {P}\mathcal {T}$-symmetric trimer: bifurcations, ghost states and associated dynamics
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Fractional Quantum Mechanics
- Numerical study of fractional nonlinear Schrödinger equations
- Stability of vortex solitons in the cubic-quintic model
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
- Two-dimensional fractional \(\mathcal{PPT}\)-symmetric cubic-quintic NLS equation: double-loop symmetry breaking bifurcations, ghost states and dynamics
- Basic fractional nonlinear-wave models and solitons
- Spontaneous symmetry breaking and ghost states supported by the fractional \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equation
This page was built for publication: Formation and propagation of fundamental and vortex soliton families in 1D and 2D dual-Lévy-index fractional nonlinear Schrödinger equations with cubic-quintic nonlinearity
