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SUMMARY:Ranis Ibragimov (Mathematics & Computer Science\, De Gruyter\, Bos
 ton\, MA\, USA)
DTSTART:20231214T123000Z
DTEND:20231214T133000Z
DTSTAMP:20260423T021332Z
UID:mmandim/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/65/"
 >Invariant Solutions of Nonlinear Mathematical Modeling of Natural Phenome
 na</a>\nby Ranis Ibragimov (Mathematics & Computer Science\, De Gruyter\, 
 Boston\, MA\, USA) as part of Mathematical models and integration methods\
 n\n\nAbstract\nThe main objective is to demonstrate the advantages of the 
 invariance method in obtaining new exact analytic solutions expressed in t
 erms of elementary functions for various physical phenomena. As one partic
 ular application of the invariance method will be the mathematical modelin
 g of oceanic and atmospheric whirlpools causing weather instabilities and\
 , possibly\, linked with climate change. As another particular example\, i
 t will be demonstrated that the invariance method allows to obtain the exa
 ct solutions of fully nonlinear Navier-Stokes equations within a thin rota
 ting atmospheric shell that serves as a simple mathematical description of
  an atmospheric circulation caused by the temperature difference between t
 he equator and the poles with included equatorial flows modeling heat wave
 s\, known as Kelvin Waves. Special attention will be given to analyzing an
 d visualizing the conserved densities associated with obtained exact solut
 ions. As another modeling scenario\, the exact solution of the shallow wat
 er equations simulating equatorial atmospheric waves of planetary scales w
 ill be analyzed and visualized.\n
LOCATION:https://researchseminars.org/talk/mmandim/65/
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