2023/02/22 by Zhu, Jian-Zhou
#FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.2302.12025
Alternating the signs of the frequencies for Fourier components with even and odd (normalized) wavenumbers in the Korteweg-de Vries (KdV) equation maintains a dispersive shock with two-sided similar oscillations (like some plasma and quantum shocks). Such a modification, referred to as the even-odd-alternating KdV (aKdV) model, can also lead to fractalization and quantum revival (Talbot effect). Further refinement to introduce "boy-girl-twin" frequencies eliminates the disturbances on shock propagation caused by the even-odd asymmetry in the dispersion. Solitonic structures, including the shock as a "shocliton," are prominently present. The traveling-wave solutions and on-torus invariants for quasi-periodic tori, for the Hamiltonian dynamics with the integrability structures broken (such as the loss of infinitely many invariants), are proposed to account for the (pseudo-)periodicity in the aKdV space-time patterns which correspond to presumably whiskered tori.