BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexey Samokhin DTSTART:20200518T120000Z DTEND:20200518T140000Z DTSTAMP:20260423T005850Z UID:GDEq/4 DESCRIPTION:Title: Usi ng the KdV conserved quantities in problems of splitting of initial data a nd reflection / refraction of solitons in varying dissipation and/or dis persion media\nby Alexey Samokhin as part of Geometry of differential equations seminar\n\n\nAbstract\nAn arbitrary compact-support initial datu m for the Korteweg-de Vries equation asymptotically splits into solitons a nd a radiation tail\, moving in opposite direction. We give a simple metho d to predict the number and amplitudes of resulting solitons and some inte gral characteristics of the tail using only conservation laws.\n\nA simila r technique allows to predict details of the behavior of a soliton which\ , while moving in non-dissipative and dispersion-constant medium encounter s a finite-width barrier with varying dissipation and/or dispersion\; be yond the layer dispersion is constant (but not necessarily of the same val ue) and dissipation is null. The process is described with a special typ e generalized KdV-Burgers equation $u_t=(u^2+f(x)u_{xx})_x$.\n\nThe transm itted wave either retains the form of a soliton (though of different param eters) or scatters a into a number of them. And a reflection wave may be n egligible or absent. This models a situation similar to a light passing fr om a humid air to a dry one through the vapor saturation/condensation area . Some rough estimations for a prediction of an output are given using the relative decay of the KdV conserved quantities\; in particular a formula for a number of solitons in the transmitted signal is given.\n LOCATION:https://researchseminars.org/talk/GDEq/4/ END:VEVENT END:VCALENDAR