Existence and stability of quasi-periodic breathers in networks of Ginzburg--Landau oscillators

DOI10.1016/j.physd.2006.12.010zbMath1179.37102OpenAlexW2050833748MaRDI QIDQ875461

Xiao Ping Yuan, Kwok Wai Chung

Publication date: 13 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.physd.2006.12.010

zbMATH Keywords

KAM theoryHamiltonian systemdissipative systemGinzburg--Landau oscillatorsquasi-periodic breather

Mathematics Subject Classification ID

Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Lattice dynamics; integrable lattice equations (37K60) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items

Quasi-periodic solution for the complex Ginzburg-Landau equation with continuous spectrum, The relation between the size of perturbations and the dimension of tori in an infinite-dimensional KAM theorem of Pöschel, Exact front, soliton and hole solutions for a modified complex Ginzburg-Landau equation from the harmonic balance method, Existence of 3-dimensional tori for 1D complex Ginzburg-Landau equation via a degenerate KAM theorem, Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices

Cites Work

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• Small divisors with spatial structure in infinite dimensional Hamiltonian systems
• Breathers in nonlinear lattices: existence, linear stability and quantization
• Localization in disordered, nonlinear dynamical systems
• On elliptic lower dimensional tori in Hamiltonian systems
• Nearly integrable infinite-dimensional Hamiltonian systems
• Normally hyperbolic invariant manifolds in dynamical systems
• The concept of anti-integrability applied to dynamical systems and to structural and electronic models in condensed matter physics
• Construction of quasi-periodic breathers via KAM technique
• Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations
• Stability of discrete breathers
• Recent progress and outstanding problems in Hamiltonian dynamics
• Anti-integrability in dynamical and variational problems
• Complicated dynamics of scalar reaction diffusion equations with a nonlocal term
• Multisite oscillations in networks of weakly coupled autonomous oscillators
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators
• Existence and stability of 3-site breathers in a triangular lattice
• Stable multisite periodic orbits in networks of weakly coupled bistable oscillators
• Invariant manifolds
• Invariant tori for non conservative perturbations of integrable systems