BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yury Stepanyants (University of Southern Queensland\, Toowoomba\, Australia) DTSTART:20220203T110000Z DTEND:20220203T120000Z DTSTAMP:20260423T005815Z UID:mmandim/34 DESCRIPTION:Title: Formation of envelop solitary waves from the localised pulses within the Ostrovsky equation\nby Yury Stepanyants (University of Southern Queens land\, Toowoomba\, Australia) as part of Mathematical models and integrati on methods\n\n\nAbstract\nWe study the formation of envelope solitons from the Korteweg–de Vries (KdV) solitons in the long term evolution within the framework of the Ostrovsky equation. This equation was derived by L.A. Ostrovsky in 1978 for the description of weakly nonlinear oceanic waves a ffected by the Earth' rotation. Subsequently\, it became clear that this e quation is rather universal\; currently\, it is widely used for the descri ption of nonlinear waves in various media. This equation is\, apparently\, non-integrable and even does not possess steady solitary wave solutions i n application to media with negative small-scale dispersion. As has been s hown by Grimshaw and Helfrich (2008)\, long-term evolution of initial puls es in the form of small-amplitude KdV soliton results in the emergence of envelope solitons which can be described by the nonlinear Schrodinger (NLS ) equation. However\, the generalised NLS equation derived by Grimshaw and Helfrich (2008) provides the results which are in contradiction with the numerical simulations. The problem was later revisited by Grimshaw and Ste panyants (2020) and was shown that the wave packet asymptotically appearin g after a long-term evolution of a KdV soliton can be described by the con ventional NLS equation. The solution obtained for an envelope soliton agre es well with the results of numerical simulations.\n LOCATION:https://researchseminars.org/talk/mmandim/34/ END:VEVENT END:VCALENDAR