Bifurcation structures and dominant modes near relative equilibria in the one-dimensional discrete nonlinear Schrödinger equation

DOI10.1016/j.physd.2009.01.001zbMath1160.37376OpenAlexW2022441500MaRDI QIDQ1016248

Carlos L. Pando L., Eusebius J. Doedel

Publication date: 5 May 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.01.001

zbMATH Keywords

Hamiltonian systemsBose-Einstein condensateHamiltonian reductionbreatherdiscrete nonlinear Schrödinger equation (DNLSE)

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items

Continuation of normal modes in finite NLS lattices, Global bifurcation of polygonal relative equilibria for masses, vortices and dNLS oscillators, Global bifurcation of travelling waves in discrete nonlinear Schrödinger equations

Uses Software

• AUTO
• AUTO-07P

Cites Work

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• Soliton trains and vortex streets as a form of Cerenkov radiation in trapped Bose-Einstein condensates
• Regular and chaotic dynamics.
• Singularities and groups in bifurcation theory. Volume II
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Embedology
• Frequency analysis for multi-dimensional systems. Global dynamics and diffusion
• Detection of Arnold diffusion in Hamiltonian systems
• Hamiltonian systems near relative equilibria
• Continuation of periodic orbits in conservative and Hamiltonian systems
• Lyapunov exponents for the \(n=3\) discrete self-trapping equation
• Induced intensity correlations in arrays of coupled Kerr waveguides
• Normal modes for nonlinear Hamiltonian systems
• Stability of nonlinear normal modes of symmetric Hamiltonian systems
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
• Hamiltonian Hopf bifurcations in the discrete nonlinear Schrödinger trimer: oscillatory instabilities, quasi-periodic solutions and a  new  type of self-trapping transition
• Nonintegrable Schrödinger discrete breathers