BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergey Dobrokhotov and Vladimir Nazaikinskii DTSTART:20230329T162000Z DTEND:20230329T180000Z DTSTAMP:20260423T024753Z UID:GDEq/84 DESCRIPTION:Title: Ex act and asymptotic solutions of a system of nonlinear shallow water equati ons in basins with gentle shores\nby Sergey Dobrokhotov and Vladimir N azaikinskii as part of Geometry of differential equations seminar\n\nLectu re held in room 303 of the Independent University of Moscow.\n\nAbstract\n We suggest an effective approximate method for constructing solutions to p roblems with a free boundary for 1-D and 2-D-systems of nonlinear shallow water equations in basins with gentle shores. The method is a modification (and pragmatic simplification) of the Carrier-Greenspan transformation in the theory of 1-D shallow water over a flat sloping bottom. The result is as follows: approximate solutions of nonlinear equations are expressed th rough solutions of naively linearized equations via parametrically defined functions. This allows us to describe the effects of waves run-up on a sh ore and their splash. Among the applications we can mention tsunami waves\ , seiches and coastal waves. We also present a comparison of the obtained formulas with the V.A. Kalinichenko (Institute for Problems in Mechanics R AS) experiment with standing Faraday waves in an extended basin with gentl y sloping shores.\n\nJoint work with D. Minenkov.\n LOCATION:https://researchseminars.org/talk/GDEq/84/ END:VEVENT END:VCALENDAR