Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude

DOI10.1512/iumj.2020.69.7845zbMath1450.35055arXiv1710.03936OpenAlexW2998404753WikidataQ114053252 ScholiaQ114053252MaRDI QIDQ5109044

Sylvie Benzoni-Gavage, Colin Mietka, Luis Miguel Rodrigues

Publication date: 7 May 2020

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.03936

zbMATH Keywords

Morse indexHamiltonian dynamicsorbital stabilityspectral stabilityperiodic traveling wavessoliton asymptoticsabbreviated action integralharmonic limit

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton equations (35Q51) Traveling wave solutions (35C07) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Related Items (3)

Spectral instability of small-amplitude periodic waves of the electronic Euler–Poisson system ⋮ Modulated equations of Hamiltonian PDEs and dispersive shocks ⋮ About plane periodic waves of the nonlinear Schrödinger equations

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