Spontaneous symmetry breaking and ghost states supported by the fractional \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equation

DOI10.1063/5.0128910MaRDI QIDQ6571788

Ming Zhong, Zhenya Yan, Pengfei Li, Li Wang

Publication date: 12 July 2024

Published in: Chaos (Search for Journal in Brave)

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX) Ordinary differential equations (34-XX)

Cites Work

• A note on the \(\mathcal PT\) invariant periodic potential \(V(x) = 4\cos^2x + 4iV_0\sin2x\)
• Fractional quantum mechanics and Lévy path integrals
• Dissipative solitons.
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• Symmetry breaking of spatial Kerr solitons in fractional dimension
• Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices
• Symmetry breaking and restoration of symmetric solitons in partially parity-time-symmetric potentials
• Spectral equivalences, Bethe ansatz equations, and reality properties in \(\mathcal{PT}\)-symmetric quantum mechanics
• Rigorous backbone of ${ \mathcal P }{ \mathcal T }$-symmetric quantum mechanics
• Revisiting the $\mathcal {P}\mathcal {T}$-symmetric trimer: bifurcations, ghost states and associated dynamics
• 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 nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations
• Nonlinear Schrödinger equation for a ${\mathcal{PT}}$-symmetric delta-function double well
• Can Parity‐Time‐Symmetric Potentials Support Families of Non‐Parity‐Time‐Symmetric Solitons?
• Stable flat-top solitons and peakons in the PT-symmetric δ -signum potentials and nonlinear media
• Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential
• Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities
• Solitons in \(\mathcal{PT}\)-symmetric systems with spin-orbit coupling and critical nonlinearity
• Stability and modulation of optical peakons in self-focusing/defocusing Kerr nonlinear media with \(\mathcal{PT}\)-\(\delta\)-hyperbolic-function potentials
• Symmetry breaking of solitons in the PT-symmetric nonlinear Schrödinger equation with the cubic-quintic competing saturable nonlinearity

Related Items (5)

Formation and propagation of fundamental and vortex soliton families in 1D and 2D dual-Lévy-index fractional nonlinear Schrödinger equations with cubic-quintic nonlinearity ⋮ Fundamental and dipole gap solitons and their dynamics in the cubic-quintic fractional nonlinear Schrödinger model with a \(\mathcal{PT}\)-symmetric lattice ⋮ On the Katugampola fractional integral and dimensional analysis of the fractal basin boundary for a random dynamical system ⋮ Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide ⋮ Modulational instability, generation, and evolution of rogue waves in the generalized fractional nonlinear Schrödinger equations with power-law nonlinearity and rational potentials

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