BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:A. V. Slunyaev (A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences\,Nizhny Novgorod\, Russia) DTSTART:20260409T110000Z DTEND:20260409T120000Z DTSTAMP:20260423T022228Z UID:mmandim/110 DESCRIPTION:Title: On the self-similar character of rogue waves\nby A. V. Slunyaev (A.V . Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of S ciences\,Nizhny Novgorod\, Russia) as part of Mathematical models and inte gration methods\n\n\nAbstract\nRogue waves are unexpectedly high waves whi ch occur seemingly without a reason on a background of waves of the modera te amplitude. Most frequently\, they are associated with the action of the nonlinear modulational instability of uniform waves with respect to weak long perturbations\, and are considered within the frameworks of the nonli near Schrödinger equation (NLSE). So-called Peregrine breathers\, which a re exact solutions of the NLSE\, are considered to be the simplest mathema tical prototypes of rogue waves. Other types of NLSE breather solutions ar e also known (named after E.A. Kuznetsov and N.N. Akhmediev). It should be noted that breather solutions have always been obtained either within the framework of the Inverse Scattering Technique or as a result of abstract mathematical constructions.\n\nWe discuss that from the general viewpoint\ , the shape of the most amplified due to the modulational instability enve lope should possess a general form. Even more\, the breather solutions are shown to be represented by fully coherent perturbations with self-similar shapes. The evolving modulations are characterized by constant values of the similarity parameter of the equation (i.e.\, the nonlinearity to dispe rsion ratio)\, just like classic solitons. Thus\, breather solutions acqui re a clear physical interpretation that is not based on the integrability property of the model. Approximate analytic breather-type solutions are ob tained for non-integrable versions of the NLSE with different orders of no nlinearity. They are verified by the direct numerical simulation of the mo dulational instability.\n\nPublications:\n\nR.M. Rozental\, A.V. Slunyaev\ , N.S. Ginzburg\, A.S. Sergeev\, I.V. Zotova\, Self-similarity of rogue wa ve generation in gyrotrons: Beyond the Peregrine breather. Chaos\, Soliton s & Fractals 183\, 114884 (2024).\n\nA.V. Slunyaev\, Breathers of the nonl inear Schrödinger equation are coherent self-similar solutions. Physica D 474\, 134575 (2025).\n\nC. Ward\, P. Kevrekidis\, Rogue waves as self-sim ilar solutions on a background: a direct calculation. Romanian J. Phys. 64 \, 112 (2019).\n LOCATION:https://researchseminars.org/talk/mmandim/110/ END:VEVENT END:VCALENDAR