Tootfinder

Space-time quasicrystals in Bose-Einstein condensates
L. Friedland, A. G Shagalov
https://arxiv.org/abs/2403.14382 https://arxiv.org/…

Space-time quasicrystals in Bose-Einstein condensates
An autoresonant approach for exciting space-time quasicrystals in Bose-Einstein condensates is proposed by employing two-component chirped frequency parametric driving or modulation of the interaction strength within Gross-Pitaevskii equation. A weakly nonlinear theory of the process is developed using Whitham's averaged variational principle yielding reduction to a two-degrees-of-freedom dynamical system in action-angle variables. Additionally, the theory also delineates permissible driving pa…

Integrable Approximations of Dispersive Shock Waves of the Granular Chain
C. Chong, A. Geisler, P. G. Kevrekidis, G. Biondini
https://arxiv.org/abs/2402.08218

Integrable Approximations of Dispersive Shock Waves of the Granular Chain
In the present work we revisit the shock wave dynamics in a granular chain with precompression. By approximating the model by an $α$-Fermi-Pasta-Ulam-Tsingou chain, we leverage the connection of the latter in the strain variable formulation to two separate integrable models, one continuum, namely the KdV equation, and one discrete, namely the Toda lattice. We bring to bear the Whitham modulation theory analysis of such integrable systems and the analytical approximation of their dispersive sho…