2017/07/26 by Ben Craps, Oleg Evnin, Vincent Luyten · 1 citation
Mathematics · Physics and Astronomy · #Angular momentum #Cold Atom Physics and Bose-Einstein Condensates #Conformal map #Decoupling (probability) #Hamiltonian (control theory) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Quartic function #SPHERES #gr-qc #hep-th #math-ph #math.AP #math.MP #nlin.SI
paper · pdf · doi:10.1007/jhep09(2017)059
published as JHEP 1709 (2017) 059 · 17 pages
arxiv created 2017/07/26 · openalex created_date 2017/07/31 · openalex publication_date 2017/09/01 · arxiv updated 2017/09/18 · openalex updated_date 2026/08/05
We study the cubic wave equation in AdS d+1 (and a closely related cubic wave equation on S 3) in a weakly nonlinear regime. Via time-averaging, these systems are accurately described by simplified infinite-dimensional quartic Hamiltonian systems, whose structure is mandated by the fully resonant spectrum of linearized perturbations. The maximally rotating sector, comprising only the modes of maximal angular momentum at each frequency level, consistently decouples in the weakly nonlinear regime. The Hamiltonian systems obtained by this decoupling display remarkable periodic return behaviors closely analogous to what has been demonstrated in recent literature for a few other related equations (the cubic Szegő equation, the conformal flow, the LLL equation). This suggests a powerful underlying analytic structure, such as integrability. We comment on the connection of our considerations to the Gross-Pitaevskii equation for harmonically trapped Bose-Einstein condensates.