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SUMMARY:Oleg Morozov
DTSTART:20231101T162000Z
DTEND:20231101T180000Z
DTSTAMP:20260423T023044Z
UID:GDEq/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/99/">Ex
 tensions of Lie algebras and integrability of some equations of fluid dyna
 mics and magnetohydrodynamics.</a>\nby Oleg Morozov as part of Geometry of
  differential equations seminar\n\nLecture held in room 303 of the Indepen
 dent University of Moscow.\n\nAbstract\nWe find the twisted extension of t
 he symmetry algebra of the 2D Euler equation in the vorticity form and use
  it to construct new Lax representation for this equation. Then we conside
 r the transformation Lie-Rinehart algebras generated by finite-dimensional
  subalgebras of the symmetry algebra and employ them to derive a family of
  Lax representations for the Euler equation. The family depends on functio
 nal parameters and contains a non-removable spectral parameter. Furthermor
 e we exhibit Lax representations for the reduced magnetohydrodynamics equa
 tions (or the Kadomtsev-Pogutse equations)\, the ideal magnetohydrodynamic
 s equations\, the quasigeostrophic two-layer model equations\, and the Cha
 rney-Obukhov equation for the ocean.\n
LOCATION:https://researchseminars.org/talk/GDEq/99/
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