Travelling breathers in Klein-Gordon lattices as homoclinic orbits to \(p\)-tori

DOI10.1007/s10884-005-8268-7zbMath1089.37045OpenAlexW2051211186MaRDI QIDQ818883

Yannick Sire

Publication date: 21 March 2006

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-005-8268-7

zbMATH Keywords

travelling wavestravelling breatherscenter manifold reductionadvance-delay differential equations

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit ⋮ Travelling breathers and solitary waves in strongly nonlinear lattices ⋮ Breathers in oscillator chains with Hertzian interactions ⋮ Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples ⋮ Center Manifold Theory in the Context of Infinite One-Dimensional Lattices ⋮ Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein–Gordon lattices ⋮ Numerical computation of travelling breathers in Klein--Gordon chains ⋮ BREATHERS IN INHOMOGENEOUS NONLINEAR LATTICES: AN ANALYSIS VIA CENTER MANIFOLD REDUCTION ⋮ Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
• Atomic-scale localization of high-energy solitary waves on lattices
• Center manifolds of infinite dimensions. I: Main results and applications
• Center manifolds of infinite dimensions. II: Proofs of the main results
• Über maximale \(L^ p\)-Regularität für Differentialgleichungen in Banach- und Hilbert-Räumen. (On maximal \(L^ p\)-regularity for differential equations in Banach and Hilbert spaces)
• The global structure of traveling waves in spatially discrete dynamical systems
• Introduction to functional differential equations
• Solitons on lattices
• Existence theorem for solitary waves on lattices
• Solitary waves with prescribed speed on infinite lattices
• A new barrier to the existence of moving kinks in Frenkel-Kontorova lattices
• Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems
• Travelling waves in a chain of coupled nonlinear oscillators
• Moving kinks and nanopterons in the nonlinear Klein-Gordon lattice
• Polynomial normal forms with exponentially small remainder for analytic vector fields
• Mobility and reactivity of discrete breathers
• Moving discrete breathers?
• Wave-solutions of reversible systems and applications
• A criterion for non-persistence of travelling breathers for perturbations of the Ablowitz-Ladik lattice
• Effective Hamiltonian for traveling discrete breathers in the FPU chain
• Travelling breathers with exponentially small tails in a chain of nonlinear oscillators
• Reduction of quasilinear elliptic equations in cylindrical domains with applications
• Nonlinear differential–difference equations and Fourier analysis
• Effective Hamiltonian for travelling discrete breathers
• Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
• The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities

This page was built for publication: Travelling breathers in Klein-Gordon lattices as homoclinic orbits to \(p\)-tori