Growth of Perturbations to the Peaked Periodic Waves in the Camassa--Holm Equation

DOI10.1137/20M1347474zbMath1467.35042arXiv2006.09516OpenAlexW3163110718MaRDI QIDQ4990080

Aigerim Madiyeva, Dmitry E. Pelinovsky

Publication date: 28 May 2021

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

Full work available at URL: https://arxiv.org/abs/2006.09516

zbMATH Keywords

stabilityperiodic boundary conditionscharacteristics

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (9)

Stability of periodic peaked solitary waves for a cubic Camassa-Holm-type equation ⋮ Spectral Instability of Peakons in the $b$-Family of the Camassa--Holm Equations ⋮ Formation of singularity of solution to a nonlinear shallow water equation ⋮ Stability of smooth periodic travelling waves in the Camassa–Holm equation ⋮ Superharmonic instability of stokes waves ⋮ Existence of the periodic peaked solitary-wave solutions to the Camassa-Holm-Kadomtsev-Petviashvili equation ⋮ Instability of \(H^1\)-stable periodic peakons for the \(\mu\)-Camassa-Holm equation ⋮ Stability of periodic peakons for a nonlinear quartic \(\mu\)-Camassa-Holm equation ⋮ Stability of smooth solitary waves in the \(b\)-Camassa-Holm equation

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