2016/03/09 by E. R. Johnson, Johnson, Edward R., Dmitry E. Pelinovsky +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1603.02961
openalex publication_date 2016/03/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Periodic travelling waves are considered in the class of reduced Ostrovsky\nequations that describe low-frequency internal waves in the presence of\nrotation. The reduced Ostrovsky equations with either quadratic or cubic\nnonlinearities can be transformed to integrable equations of the Klein--Gordon\ntype by means of a change of coordinates. By using the conserved momentum and\nenergy as well as an additional conserved quantity due to integrability, we\nprove that small-amplitude periodic waves are orbitally stable with respect to\nsubharmonic perturbations, with period equal to an integer multiple of the\nperiod of the wave. The proof is based on construction of a Lyapunov\nfunctional, which is convex at the periodic wave and is conserved in the time\nevolution. We also show numerically that convexity of the Lyapunov functional\nholds for periodic waves of arbitrary amplitudes.\n