Existence and numerical approximation of periodic motions of an infinite lattice of particles

DOI10.1007/BF00917876zbMath0838.34046MaRDI QIDQ1905436

Gianni Arioli, Gazzola, Filippo

Publication date: 30 May 1996

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

infinite latticesperiodic non constant solution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Dynamics of a system of particles, including celestial mechanics (70F99)

Related Items (15)

Ground states for infinite lattices with nearest neighbor interaction ⋮ Breathers on diatomic Fermi-Pasta-Ulam lattices ⋮ Multibump periodic motions of an infinite lattice of particles ⋮ Solitary waves with prescribed speed on infinite lattices ⋮ Existence and Stability of Odd and Even Parity Discrete Breathers in Fermi--Pasta--Ulam Lattices ⋮ Multiple periodic solutions for lattice dynamical systems with superquadratic potentials ⋮ Nontrivial periodic motions for resonant type asymptotically linear lattice dynamical systems ⋮ Periodic motions for FPU lattice systems with asymptotically quadratic potentials ⋮ Periodic motions of a class of forced infinite lattices with nearest neighbor interaction ⋮ Unnamed Item ⋮ Some breathers and multi-breathers for FPU-type chains ⋮ Multiple periodic solutions for two-dimensional lattice dynamic systems ⋮ Existence of odd, even, and multi-pulse discrete breathers in infinite Fermi-Pasta-Ulam lattices ⋮ The existence of periodic solutions for a class of nonautonomous lattices with bounded-coupling ⋮ A new mathematical explanation of what triggered the catastrophic torsional mode of the tacoma narrows bridge

Cites Work

• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Critical point theorems for indefinite functionals
• Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits
• Theory of nonlinear lattices.
• On periodic motions of lattices of Toda type via critical point theory
• Multibump periodic motions of an infinite lattice of particles
• Dual variational methods in critical point theory and applications
• Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
• Periodic motions of an infinite lattice of particles with nearest neighbor interaction
• A mountain pass method for the numerical solution of semilinear elliptic problems

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