Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler

DOI10.1088/1751-8121/AA96F4zbMath1387.81396arXiv1710.03292OpenAlexW2763476382MaRDI QIDQ4606143

Dmitry A. Zezyulin, Vladimir V. Konotop

Publication date: 1 March 2018

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.03292

zbMATH Keywords

HamiltoniandissipationnonlinearitysolitonsPT symmetry

Mathematics Subject Classification ID

Unified quantum theories (81V22) Quantum optics (81V80) NLS equations (nonlinear Schrödinger equations) (35Q55) Many-body theory; quantum Hall effect (81V70) Exactly and quasi-solvable systems arising in quantum theory (81U15) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Soliton solutions (35C08)

Related Items (1)

Modulated solitons, soliton and vortex clusters in purely nonlinear defocusing media

Cites Work

• \({\mathcal{PT}}\)-symmetric periodic optical potentials
• The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field
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• Exact first-order solutions of the nonlinear Schrödinger equation
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• Hamiltonian structure for a modified discrete self-trapping dimer
• Water waves, nonlinear Schrödinger equations and their solutions
• Long-time stability of breathers in Hamiltonian ${ \mathcal P }{ \mathcal T }$-symmetric lattices
• Dimer with gain and loss: Integrability and ${\mathcal{P}}{\mathcal{T}}$-symmetry restoration
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• 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
• Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity
• An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss
• On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance
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