The Nonlinear Schrödinger Equation for the Delta-Comb Potential: Quasi-Classical Chaos and Bifurcations of Periodic Stationary Solutions

DOI10.1142/S1402925109000145zbMath1177.35229arXivcond-mat/0506645MaRDI QIDQ3395361

Kevin Rapedius, Hans Jürgen Korsch, Dirk Witthaut

Publication date: 26 August 2009

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0506645

zbMATH Keywords

chaosnonlinear Schrödinger equationHamiltonian systemsbifurcationsGross-Pitaevskii equationBose-Einstein condensateperiod doublingnonlinear Bloch bands

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Periodic solutions to PDEs (35B10) Quantum optics (81V80) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

Related Items (8)

Coding of Nonlinear States for NLS-Type Equations with Periodic Potential ⋮ Tunnel effect and analysis of the survival amplitude in the nonlinear Winter's model ⋮ Coding of nonlinear states for the Gross-Pitaevskii equation with periodic potential ⋮ Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method ⋮ On the chaotic dynamics in two coupled partial differential equations for evolution of surface plasmon polaritons ⋮ Nonlinear models and bifurcation trees in quantum mechanics: a review of recent results ⋮ Analytical Solitary Wave Solutions of a Nonlinear Kronig-Penney Model for Photonic Structures Consisting of Linear and Nonlinear Layers ⋮ Regular and chaotic solutions in BEC for tilted bichromatical optical lattice

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Anticipated tax reforms and temporary tax cuts: a general equilibrium analysis
• Crossing scenario for a nonlinear non-Hermitian two-level system
• Stationary solutions of the Gross-Pitaevskii equation with linear counterpart
• Bifurcations of periodic trajectories in non-integrable Hamiltonian systems with two degrees of freedom: Numerical and analytical results
• Bifurcation of 4:1 subharmonics in the nonlinear Mathieu equation
• PT-symmetry in one-dimensional quantum periodic potentials
• Elliptic functions and applications
• Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii equation
• Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure
• Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
• Bifurcation of solutions of nonlinear boundary value problems
• Limit Cycle Oscillations of Parametrically Excited Second-Order Nonlinear Systems
• Bound states in a nonlinear Kronig - Penney model
• Bound and resonance states of the nonlinear Schrödinger equation in simple model systems
• The band spectrum of periodic potentials with Script PScript T-symmetry
• Elastic scattering of a quantum matter-wave bright soliton on a barrier
• Nonlinear modes for the Gross–Pitaevskii equation—a demonstrative computation approach
• A perturbative analysis of modulated amplitude waves in Bose–Einstein condensates
• The transition from diffusion to blow-up for a nonlinear Schrödinger equation in dimension 1

This page was built for publication: The Nonlinear Schrödinger Equation for the Delta-Comb Potential: Quasi-Classical Chaos and Bifurcations of Periodic Stationary Solutions