Justification of the log--KdV Equation in Granular Chains: The Case of Precompression

DOI10.1137/140969270zbMath1317.34020arXiv1405.3385OpenAlexW2964289960MaRDI QIDQ5179171

Eric Dumas, Dmitry E. Pelinovsky

Publication date: 19 March 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.3385

zbMATH Keywords

Korteweg-de Vries equationFermi-Pasta-Ulam latticejustification of amplitude equationsexistence and stability of nonlinear waves

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary lattice differential equations (34A33)

Related Items (12)

Orbital stability of periodic traveling-wave solutions for the log-KdV equation ⋮ Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons ⋮ Solitary waves in FPU-type lattices ⋮ Nonlinear stability of periodic-wave solutions for systems of dispersive equations ⋮ KP-II Approximation for a Scalar Fermi–Pasta–Ulam System on a 2D Square Lattice ⋮ Long-time approximations of small-amplitude, long-wavelength FPUT solutions ⋮ High-energy waves in superpolynomial FPU-type chains ⋮ Long-time stability of small FPU solitary waves ⋮ Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations ⋮ The structure of algebraic solitons and compactons in the generalized Korteweg-de Vries equation ⋮ Justification of the KP-II approximation in dynamics of two-dimensional FPU systems ⋮ Traveling fronts in dissipative granular chains and nonlinear lattices

This page was built for publication: Justification of the log--KdV Equation in Granular Chains: The Case of Precompression