BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:K.R. Khusnutdinova (Department of Mathematical Sciences\, Loughbor ough University\, UK) DTSTART:20230427T110000Z DTEND:20230427T120000Z DTSTAMP:20260423T005810Z UID:mmandim/56 DESCRIPTION:Title: On elliptic cylindrical Kadomtsev-Petviashvili equation for surface waves \nby K.R. Khusnutdinova (Department of Mathematical Sciences\, Loughbo rough University\, UK) as part of Mathematical models and integration meth ods\n\n\nAbstract\nThere exist two classical versions of the Kadomtsev-Pet viashvili (KP) equation [1]\, related to the Cartesian and cylindrical geo metries of the waves (derivations for surface waves were given in [2] and [3]\, respectively). We derived and studied a version related to the ellip tic-cylindrical geometry in [4] (joint work with Klein\, Matveev and Smirn ov). The derivation was given from the full set of Euler equations for sur face gravity waves with the account of surface tension. The ecKP equation contains a parameter\, and it reduces to the cKP equation both when this p arameter tends to zero\, and when the solutions are considered at distance s much larger than that parameter. We showed that there exist transformati ons between all three versions of the KP equation associated with the phys ical problem formulation (KP\, cKP and ecKP equations)\, and used them to obtain new classes of approximate solutions for the Euler equations. The s olutions exist on the whole plane (at least formally). We hope that they could be useful in describing an intermediate asymptotics for the problems where sources\, boundaries and obstacles have elliptic or nearly-elliptic geometry.\n\nReferences:\n\n[1] B.P. Kadomtsev\, V.I. Petviashvili\, On t he stability of solitary waves in weakly dispersing media\, Sov. Phys. Dok l.\, 15 (1970) 539-541.\n\n[2] M.J. Ablowitz and H. Segur\, On the evoluti on of packets of water waves\, J. Fluid Mech.\, 92 (1979) 691-715.\n\n[3] R.S. Johnson\, Water waves and Korteweg - de Vries equations\, J. Fluid Me ch.\, 97 (1980) 701-719.\n\n[4] K.R. Khusnutdinova\, C. Klein\, V.B. Matve ev\, A.O. Smirnov\, On the integrable elliptic cylindrical Kadomtsev-Petvi ashvili equation\, Chaos 23 (2013) 013126.\n LOCATION:https://researchseminars.org/talk/mmandim/56/ END:VEVENT END:VCALENDAR