Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein–Gordon lattices
From MaRDI portal
Publication:3584652
DOI10.1080/00036811003627518zbMath1203.37121arXiv0909.3467OpenAlexW1976342751WikidataQ58251664 ScholiaQ58251664MaRDI QIDQ3584652
Tiziano Penati, Simone Paleari, Dario Bambusi
Publication date: 30 August 2010
Published in: Applicable Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0909.3467
Periodic solutions to ordinary differential equations (34C25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Lattice dynamics; integrable lattice equations (37K60)
Related Items
On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice ⋮ Existence of exponentially and superexponentially spatially localized breather solutions for nonlinear klein–gordon lattices in ℤd, d ≥ 1 ⋮ Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators ⋮ Multibreathers in Klein-Gordon chains with interactions beyond nearest neighbors ⋮ Existence and Asymptotic Stability of Quasi-Periodic Solutions of Discrete NLS with Potential ⋮ Breather solutions in periodic media ⋮ On the nonexistence of degenerate phase-shift multibreathers in Klein-Gordon models with interactions beyond nearest neighbors ⋮ Reduction of a damped, driven Klein–Gordon equation into a discrete nonlinear Schrödinger equation: Justification and numerical comparison ⋮ Breather solutions for inhomogeneous FPU models using Birkhoff normal forms ⋮ Localised time-periodic solutions of discrete nonlinear Klein-Gordon systems with convex on-site potentials ⋮ Existence and Stability of Klein–Gordon Breathers in the Small-Amplitude Limit ⋮ Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations ⋮ Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction ⋮ Existence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approach
Cites Work
- Travelling breathers in Klein-Gordon lattices as homoclinic orbits to \(p\)-tori
- On metastability in FPU
- Stability theory of solitary waves in the presence of symmetry. I
- Centre manifold reduction for quasilinear discrete systems
- Travelling waves in a chain of coupled nonlinear oscillators
- Quasiperiodic breathers in Hamiltonian lattices with symmetries
- Families of periodic orbits for some PDE's in higher dimensions.
- Normal form for travelling kinks in discrete Klein-Gordon lattices
- Travelling breathers with exponentially small tails in a chain of nonlinear oscillators
- Asymptotic stability of Toda lattice solitons
- Counter-propagating two-soliton solutions in the Fermi–Pasta–Ulam lattice
- Boundary effects on the dynamics of chains of coupled oscillators
- Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators
- The validity of modulation equations for extended systems with cubic nonlinearities
- Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
- Excitation thresholds for nonlinear localized modes on lattices
- Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators
- Travelling waves in the Fermi-Pasta-Ulam lattice
- Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
- Localized waves in nonlinear oscillator chains
- Continuous approximation of breathers in one- and two-dimensional DNLS lattices
- Families of periodic solutions of resonant PDEs
- Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems.