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SUMMARY:Mats Vermeeren
DTSTART:20250718T080000Z
DTEND:20250718T090000Z
DTSTAMP:20260423T010620Z
UID:nmps/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/nmps/11/">La
 grangian multiforms and conservation laws</a>\nby Mats Vermeeren as part o
 f Nagoya Math-Phys Seminar\n\n\nAbstract\nLagrangian multiform theory is a
  variational principle for hierarchies of commuting differential equations
 . Lagrangian 1-forms typically describe systems of commuting ODEs\, Lagran
 gian 2-forms typically describe hierarchies of (1+1)-dimensional PDEs\, an
 d so on. Typical examples include soliton hierarchies such as the KdV. In 
 these examples\, there is a close relation between the existence of a Lagr
 angian multiform and the fact that the flows are variational symmetries of
  each other.\n\n In this talk\, we give a number of examples of Lagrangian
  multiforms that break this pattern. We will present Lagrangian 2-forms th
 at can be interpreted as conservation laws for 3-dimensional PDEs. In thes
 e examples\, the conservation Law does not arise via Noether's theorem fro
 m a known Lagrangian. Almost the opposite is true: the construction of a L
 agrangian multiform relies on the existence of a suitable conservation Law
  for an equation that is not variational by itself.\n\nWe also give additi
 onal examples of Lagrangian multiforms for dispersionless integrable syste
 ms\, including some systems that arise via hydrodynamic reductions of Pleb
 anski's second heavenly equation.\n
LOCATION:https://researchseminars.org/talk/nmps/11/
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