Dimer with gain and loss: Integrability and ${\mathcal{P}}{\mathcal{T}}$-symmetry restoration

DOI10.1088/1751-8113/48/32/325201zbMath1329.35275arXiv1506.08229OpenAlexW3125027235WikidataQ113091424 ScholiaQ113091424MaRDI QIDQ3447659

Philippe Dubard, Dmitry E. Pelinovsky, Igor V. Barashenkov

Publication date: 27 October 2015

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

Full work available at URL: https://arxiv.org/abs/1506.08229

zbMATH Keywords

Hamiltonian structurecomplete integrability\(\mathcal{PT}\)-symmetrygain and lossspontaneous symmetry restorationnonlinear Schrödinger dimertrajectory confinement

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (13)

Nonlinear wave dynamics near phase transition in \(\mathcal{PT}\)-symmetric localized potentials ⋮ Integrability and trajectory confinement in -symmetric waveguide arrays ⋮ Sublattice Signatures of Transitions in a $$\mathscr {PT}$$ PT -Symmetric Dimer Lattice ⋮ Coupled pendula chains under parametric \(\mathcal{PT}\)-symmetric driving force ⋮ On integrable wave interactions and Lax pairs on symmetric spaces ⋮ Balanced loss-gain induced chaos in a periodic Toda lattice ⋮ Integrable oscillator type and Schrödinger type dimers ⋮ Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler ⋮ Nonlinear waves in an anti-Hermitian lattice with cubic nonlinearity ⋮ Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces ⋮ Spinor solitons and their \(\mathcal{PT}\)-symmetric offspring ⋮ Stability, integrability, and nonlinear dynamics of PT-symmetric optical couplers with cubic cross-interactions or cubic-quintic nonlinearities ⋮ The \(N\)-wave equations with \(\mathcal{PT}\) symmetry

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