Center Manifold Theory in the Context of Infinite One-Dimensional Lattices

DOI10.1007/978-3-540-72995-2_6zbMath1151.82323OpenAlexW1793292710MaRDI QIDQ3529221

Guillaume James, Yannick Sire

Publication date: 20 October 2008

Published in: The Fermi-Pasta-Ulam Problem (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-72995-2_6

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

Travelling breathers and solitary waves in strongly nonlinear lattices ⋮ Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples ⋮ Moving Modulating Pulse and Front Solutions of Permanent Form in a FPU Model with Nearest and Next-to-Nearest Neighbor Interaction ⋮ Periodic travelling wave solutions of discrete nonlinear Schrödinger equations ⋮ Stable manifolds to bounded solutions in possibly ill-posed PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Travelling breathers in Klein-Gordon lattices as homoclinic orbits to \(p\)-tori
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• 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 Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Nonlinear coherent structures in physics and biology. Proceedings of the 7th interdisciplinary workshop, held at Dijon, France, 4-6 June, 1991
• Existence theorem for solitary waves on lattices
• Solitary waves with prescribed speed on infinite lattices
• Centre manifold reduction for quasilinear discrete systems
• 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
• Travelling waves in FPU lattices
• Bifurcations of travelling wave solutions in the discrete NLS equations
• Numerical computation of travelling breathers in Klein--Gordon chains
• Mobility and reactivity of discrete breathers
• Wave-solutions of reversible systems and applications
• Travelling breathers in Klein-Gordon chains
• Breathers on diatomic Fermi-Pasta-Ulam lattices
• Tangent bifurcation of band edge plane waves, dynamical symmetry breaking and vibrational localization
• Travelling breathers with exponentially small tails in a chain of nonlinear oscillators
• The parameterization method for invariant manifolds. III: Overview and applications
• Existence of breathers on FPU lattices
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Solitary waves on FPU lattices: II. Linear implies nonlinear stability
• Method for Solving the Korteweg-deVries Equation
• Reduction of quasilinear elliptic equations in cylindrical domains with applications
• A numerical calculation of a weakly non-local solitary wave: the ϕ⁴breather
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• The parameterization method for invariant manifolds II: regularity with respect to parameters
• Solitary waves on Fermi–Pasta–Ulam lattices: III. Howland-type Floquet theory
• Travelling waves in the Fermi-Pasta-Ulam lattice
• Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
• Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems
• The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities
• Existence of breathers in classical ferromagnetic lattices
• Korteweg–de Vries equation and energy sharing in Fermi–Pasta–Ulam
• Discrete breathers in Fermi–Pasta–Ulam lattices
• Localized waves in nonlinear oscillator chains
• Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems.

This page was built for publication: Center Manifold Theory in the Context of Infinite One-Dimensional Lattices