Stationary modes and integrals of motion in nonlinear lattices with a ${\mathcal {PT}}$-symmetric linear part

DOI10.1088/1751-8113/46/41/415301zbMath1281.82030arXiv1306.5286OpenAlexW3098804230MaRDI QIDQ2861465

Dmitry A. Zezyulin, Vladimir V. Konotop

Publication date: 8 November 2013

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

Full work available at URL: https://arxiv.org/abs/1306.5286

zbMATH Keywords

bifurcationparty-time symmetric operator

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Bifurcations of singular points in dynamical systems (37G10) Antennas, waveguides in optics and electromagnetic theory (78A50) Statistical mechanics of solids (82D20) Lasers, masers, optical bistability, nonlinear optics (78A60) Nonlinear ordinary differential operators (34L30)

Related Items (8)

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 ⋮ Symmetries and invariants for non-Hermitian Hamiltonians ⋮ Global existence of solutions to coupled \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equations ⋮ 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 ⋮ Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

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