Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation

DOI10.3934/dcds.2015.35.225zbMath1304.35638arXiv1311.6715OpenAlexW2067846789MaRDI QIDQ479972

Roy H. Goodman, Jeremy L. Marzuola, Michael I. Weinstein

Publication date: 8 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6715

zbMATH Keywords

nonlinear Schrödinger equationHamiltonian systemstunnelingshadowingeffective dynamics

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60) Bifurcations in context of PDEs (35B32)

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Uses Software

• DLMF

Cites Work

• Normal form for the symmetry-breaking bifurcation in the nonlinear Schrödinger equation
• Collapsing estimates and the rigorous derivation of the 2d cubic nonlinear Schrödinger equation with anisotropic switchable quadratic traps
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• Double wells
• Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
• Stability analysis for pitchfork bifurcations of solitary waves in generalized nonlinear Schrödinger equations
• On the rigorous derivation of the 3D cubic nonlinear Schrödinger equation with a quadratic trap
• Behavior of Hamiltonian systems close to integrable
• Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes
• Symmetry-Breaking Bifurcation in Nonlinear Schrödinger/Gross–Pitaevskii Equations
• Jacobi Elliptic Functions from a Dynamical Systems Point of View
• Classification of Solitary Wave Bifurcations in Generalized Nonlinear Schrödinger Equations
• Three Is a Crowd: Solitary Waves in Photorefractive Media with Three Potential Wells
• Hierarchy of bifurcations in the truncated and forced nonlinear Schrödinger model
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