Long-time approximations of small-amplitude, long-wavelength FPUT solutions

DOI10.3934/dcds.2023131arXiv2306.14999OpenAlexW4388113182MaRDI QIDQ6195930

C. Eugene Wayne, Trevor Norton

Publication date: 14 March 2024

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

Full work available at URL: https://arxiv.org/abs/2306.14999

zbMATH Keywords

modified Korteweg-de Vries equationlong-time stabilitykink solutionsFermi-Pasta-Ulam-Tsingou latticesmall-amplitude approximations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lattice dynamics; integrable lattice equations (37K60)

Cites Work

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• Long-time stability of small FPU solitary waves
• Solutions of mKdV in classes of functions unbounded at infinity
• On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system
• Solitary waves in FPU-type lattices
• Action minimising fronts in general FPU-type chains
• Heteroclinic Travelling Waves in Convex FPU-Type Chains
• Solitary waves on FPU lattices: II. Linear implies nonlinear stability
• Existence of Dynamic Phase Transitions in a One-Dimensional Lattice Model with Piecewise Quadratic Interaction Potential
• Solitary waves on Fermi–Pasta–Ulam lattices: III. Howland-type Floquet theory
• Solitary waves on Fermi–Pasta–Ulam lattices: IV. Proof of stability at low energy
• Travelling waves in the Fermi-Pasta-Ulam lattice
• Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
• Supersonic kinks and solitons in active solids
• Justification of the log--KdV Equation in Granular Chains: The Case of Precompression
• The β Fermi-Pasta-Ulam-Tsingou recurrence problem
• Kinetics of Martensitic Phase Transitions: Lattice model
• Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory