Localised Nonlinear Modes in the PT-Symmetric Double-Delta Well Gross-Pitaevskii Equation

DOI10.1007/978-3-319-31356-6_8zbMath1402.81125arXiv1511.06599OpenAlexW3102446554MaRDI QIDQ4555424

Dmitry A. Zezyulin, Igor V. Barashenkov

Publication date: 20 November 2018

Published in: Springer Proceedings in Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.06599

zbMATH Keywords

return timetranscendental equationnonlinear modenormalisation constraintsmall positive root

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (5)

\(\mathcal{PT}\)-symmetric peakon solutions in self-focusing/defocusing power-law nonlinear media: stability, interactions and adiabatic excitations ⋮ 𝒫𝒯-symmetric and antisymmetric nonlinear states in a split potential box ⋮ Soliton formation and dynamics in the quintic nonlinear media with \(\mathcal{PT}\)-invariant harmonic-Gaussian potential ⋮ Stable solitons and peakons, quantum information entropies, interactions, and excitations for generalized \(\mathcal{PT}\)-symmetric NLS equations ⋮ Stable flat-top solitons and peakons in the PT-symmetric δ -signum potentials and nonlinear media

Cites Work

• Bound state solutions of the Schrödinger equation for a \(\mathcal{PT}\)-symmetric potential with Dirac delta functions
• Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii equation
• Visualization of Branch Points in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Waveguides
• Analytical solutions to a class of nonlinear Schrödinger equations with {\cal PT} -like potentials
• Nonlinear Schrödinger equation for a ${\mathcal{PT}}$-symmetric delta-function double well
• An explicitly solvable model of the spontaneous PT-symmetry breaking
• Solvability and -symmetry in a double-well model with point interactions

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