BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Konstantin Druzhkov DTSTART:20241211T162000Z DTEND:20241211T180000Z DTSTAMP:20260423T024833Z UID:GDEq/123 DESCRIPTION:Title: I nvariant reduction for PDEs. I: Conservation laws of 1+1 systems of evolut ion equations\nby Konstantin Druzhkov as part of Geometry of different ial equations seminar\n\n\nAbstract\nAmong various methods for constructin g exact solutions of partial differential equations\, the symmetry-invaria nt approach is particularly noteworthy. This method is especially effectiv e in the case of point symmetries\, but when it comes to higher symmetries \, additional steps are required to obtain invariant solutions. It turns o ut that systems that describe symmetry-invariant solutions inherit symmetr y-invariant geometric structures even in the case of higher symmetries. Mo reover\, the reduction of invariant conservation laws of 1+1 systems of ev olution equations can be described as an algorithm and implemented in Mapl e. Starting from invariant conservation laws\, we get constants of invaria nt motion. They are analogs of first integrals of ODEs\, and one can use t hem in the same way. In particular\, a sufficient number of independent co nstants of invariant motion allows one to integrate the corresponding syst em for invariant solutions.\n LOCATION:https://researchseminars.org/talk/GDEq/123/ END:VEVENT END:VCALENDAR