Stable and oscillating solitons of \(\mathcal{PT}\)-symmetric couplers with gain and loss in fractional dimension

DOI10.1007/S11071-020-06180-7zbMath1517.35216arXiv2104.07218OpenAlexW3153355697MaRDI QIDQ6174217

Qifan Zhu, Jincheng Shi, Hu Long, Xiaowei Lu, Yi Cai, Liangwei Zeng, Jingzhen Li, Hong-Yi Chen

Publication date: 16 August 2023

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.07218

zbMATH Keywords

nonlinear Schrödinger equationfractional calculus\(\mathcal{PT}\)-symmetrycoupled solitons

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Soliton solutions (35C08) Fractional partial differential equations (35R11)

Related Items (7)

Solitons in spin-orbit-coupled systems with fractional spatial derivatives ⋮ Quadratic fractional solitons ⋮ Cubic-quartic optical soliton perturbation with complex Ginzburg-Landau equation by the enhanced Kudryashov's method ⋮ Solitons in a coupled system of fractional nonlinear Schrödinger equations ⋮ The beam control in two-channels PT-symmetric waveguide with fractional diffraction effect ⋮ Analytical novel solutions to the fractional optical dynamics in a medium with polynomial law nonlinearity and higher order dispersion with a new local fractional derivative ⋮ Parameters controlling of vortex solitons in nonlocal nonlinear medium with gradually characteristic length

Cites Work

• Unnamed Item
• Unnamed Item
• Fractional quantum mechanics and Lévy path integrals
• Accessible solitons of fractional dimension
• Modulational instability in fractional nonlinear Schrödinger equation
• 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
• Fractional quantum couplers
• Symmetry breaking of spatial Kerr solitons in fractional dimension
• One-dimensional localized modes of spin-orbit-coupled Bose-Einstein condensates with spatially periodic modulated atom-atom interactions: nonlinear lattices
• Modulated solitons, soliton and vortex clusters in purely nonlinear defocusing media
• Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices
• The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrödinger equation arising in quantum mechanics
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations ^*
• 𝓟𝓣-symmetric quantum mechanics
• Spontaneous symmetry breaking in purely nonlinear fractional systems
• 1D Solitons in Saturable Nonlinear Media with Space Fractional Derivatives
• Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities

This page was built for publication: Stable and oscillating solitons of \(\mathcal{PT}\)-symmetric couplers with gain and loss in fractional dimension