Multi-dimensional stable fundamental solitons and excitations in \(\mathcal{PT}\)-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions

DOI10.1016/j.cnsns.2017.09.014OpenAlexW2755643197MaRDI QIDQ2205744

Zhenya Yan, Yong Chen

Publication date: 21 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2017.09.014

zbMATH Keywords

interactionssoliton excitationsstable solitons\(\mathcal{PT}\)-symmetric harmonic-Gaussian potentialmulti-dimensional nonlinear Schrödinger-like equation

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Qxx) Qualitative properties of solutions to partial differential equations (35Bxx)

Related Items (6)

Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning ⋮ Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning ⋮ Stable solitons and interactions of the logarithmic nonlinear Schrödinger equation with two \(\mathcal{PT} \)-symmetric non-periodic potentials ⋮ Soliton formation and dynamics in the quintic nonlinear media with \(\mathcal{PT}\)-invariant harmonic-Gaussian potential ⋮ Stable modes of derivative nonlinear Schrödinger equation with super-Gaussian and parabolic potential ⋮ Stationary Hermite-Gaussian solitons and their control for nonlinear Schrödinger equation with complex potential

Uses Software

• Matlab

Cites Work

• Unnamed Item
• \({\mathcal{PT}}\)-symmetric periodic optical potentials
• Localized modes of the (n+1)-dimensional Schrödinger equation with power-law nonlinearities in \(\mathcal{PT}\)-symmetric potentials
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• Dynamical behaviors of optical solitons in parity-time (\(\mathcal{PT}\)) symmetric sextic anharmonic double-well potentials
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Must a Hamiltonian be Hermitian?
• Analytical solutions to a class of nonlinear Schrödinger equations with {\cal PT} -like potentials
• Spectral Methods in MATLAB
• 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
• On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT- and non-PT-symmetric potentials
• Solitons and their stability in the nonlocal nonlinear Schrödinger equation with PT-symmetric potentials
• Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential

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