Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with 𝒫𝒯-symmetry

DOI10.1017/PRM.2018.83zbMath1481.34026arXiv1702.03469OpenAlexW2963948870MaRDI QIDQ4960366

Dmitry E. Pelinovsky, Tomáš Dohnal

Publication date: 15 April 2020

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.03469

zbMATH Keywords

bifurcationspectral intervalsnonlinear bound states\(\mathcal{PT}\) -symmetrynon-selfadjoint linear Schrödinger operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (5)

Bifurcation of gap solitons in coupled mode equations in \(d\) dimensions ⋮ On nonexistence of continuous families of stationary nonlinear modes for a class of complex potentials ⋮ Spectra of operator pencils with small 𝒫𝒯-symmetric periodic perturbation ⋮ Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons ⋮ Justification of the asymptotic coupled mode approximation of out-of-plane gap solitons in Maxwell equations

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