Nonlinear Stationary States in PT-Symmetric Lattices

DOI10.1137/130912694zbMath1284.34017arXiv1303.3298OpenAlexW2080747330MaRDI QIDQ2871362

Dmitry Y. Tyugin, Dmitry E. Pelinovsky, Panayotis G. Kevrekidis

Publication date: 22 January 2014

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.3298

zbMATH Keywords

stabilityexistencebifurcationsstationary statesdiscrete nonlinear Schrödinger equationdiscrete solitonsPT-symmetric lattices

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Ordinary lattice differential equations (34A33)

Related Items (12)

Existence and stability of \(\mathcal{PT}\)-symmetric states in nonlinear two-dimensional square lattices ⋮ Nonlinear wave dynamics near phase transition in \(\mathcal{PT}\)-symmetric localized potentials ⋮ Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials ⋮ Single-hump and double-hump solitons in a symmetric complex potential ⋮ Exponential Asymptotics for Solitons in PT-Symmetric Periodic Potentials ⋮ Kink scattering from a parity-time-symmetric defect in the \(\phi^4\) model ⋮ Can Parity‐Time‐Symmetric Potentials Support Families of Non‐Parity‐Time‐Symmetric Solitons? ⋮ Bifurcation of Soliton Families from Linear Modes in Non‐‐Symmetric Complex Potentials ⋮ Necessity of \(\mathcal{PT}\) symmetry for soliton families in one-dimensional complex potentials ⋮ Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with 𝒫𝒯-symmetry ⋮ Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems ⋮ Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry

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