BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Konstantin Druzhkov DTSTART:20260415T162000Z DTEND:20260415T180000Z DTSTAMP:20260423T022228Z UID:GDEq/156 DESCRIPTION:Title: I nvariant reduction for PDEs. IV: Symmetries that rescale geometric structu res\nby Konstantin Druzhkov as part of Geometry of differential equati ons seminar\n\n\nAbstract\nFor a system of differential equations and a sy mmetry\, the framework of invariant reduction systematically computes how invariant geometric structures are inherited by the subsystem governing i nvariant solutions. In this setting\, the reduction of structures invarian t under a two-dimensional Lie algebra requires its commutativity. We exte nd this mechanism to the case where geometric structures are invariant und er one symmetry $X$ and are rescaled\, by a factor of $-a$\, by another sy mmetry $X_s$ satisfying $[X_s\, X] = aX$. As an application\, we describe a class of exact solutions to systems possessing sufficiently many symmet ries and conservation laws subject to certain compatibility conditions. Th ese solutions are invariant under pairs of symmetries and are completely d etermined by explicitly constructed functions that are constant on them\; the description is geometric and does not require any integrability-relat ed structures such as Lax pairs.\n LOCATION:https://researchseminars.org/talk/GDEq/156/ END:VEVENT END:VCALENDAR