KdV waves in atomic chains with nonlocal interactions

DOI10.3934/dcds.2016.36.2047zbMath1343.37076arXiv1503.02307OpenAlexW1922431368MaRDI QIDQ887691

Alice Mikikits-Leitner, Michael Herrmann

Publication date: 27 October 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02307

zbMATH Keywords

asymptotic analysisHamiltonian lattices with nonlocal couplingKdV limit of lattice waves

Mathematics Subject Classification ID

Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Solitary waves in FPU-type lattices ⋮ KdV-like solitary waves in two-dimensional FPU-lattices ⋮ KP-II Approximation for a Scalar Fermi–Pasta–Ulam System on a 2D Square Lattice ⋮ Solitary wave propagation in a two-dimensional lattice ⋮ Moving Modulating Pulse and Front Solutions of Permanent Form in a FPU Model with Nearest and Next-to-Nearest Neighbor Interaction ⋮ Nonlinear and nonlocal eigenvalue problems: variational existence, decay properties, approximation, and universal scaling limits ⋮ High-energy waves in superpolynomial FPU-type chains ⋮ A uniqueness result for a simple superlinear eigenvalue problem ⋮ Solitary waves on nonlocal Fermi-Pasta-Ulam lattices: exponential localization ⋮ Solitary waves in atomic chains and peridynamical media ⋮ Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains ⋮ Justification of the KP-II approximation in dynamics of two-dimensional FPU systems

Cites Work

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• A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit
• Approximation of Polyatomic FPU Lattices by KdV Equations

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