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SUMMARY:A.V. Aksenov
DTSTART:20210218T110000Z
DTEND:20210218T120000Z
DTSTAMP:20260423T005818Z
UID:mmandim/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/16/"
 >Symmetries\, conservation laws\, and exact solutions to a one-dimensional
  system of shallow water equations over an uneven bottom</a>\nby A.V. Akse
 nov as part of Mathematical models and integration methods\n\n\nAbstract\n
 The symmetries of a one-dimensional system of shallow water equations over
  an uneven bottom in Euler’s variables are classified. Based on the resu
 lts of the group classification obtained\, it is concluded that it is poss
 ible to reduce the one-dimensional system of shallow water equations to a 
 linear system of equations using point transformations only in the cases o
 f horizontal and inclined bottom profiles. We also classify the contact sy
 mmetries of the one-dimensional shallow water equation over an uneven bott
 om in Lagrangian’s variables.\n\nThe hydrodynamic conservation laws of a
  one-dimensional system of shallow water equations in Eulerian’s variabl
 es are classified. A new basic conservation law is obtained. The first-ord
 er conservation laws of the one-dimensional shallow water equation in Lagr
 angian’s variables are classified.\n\nA three-parameter family of exact 
 solutions of a one-dimensional system of shallow water equations over an i
 nclined bottom is obtained and investigated\, describing the ”step’’
  wave's arrival on the shore and its reflection from it. The nonlinear the
  overwash effect and the effect of the amplification of the incoming wave 
 when it is reflected from the shore are described.\n
LOCATION:https://researchseminars.org/talk/mmandim/16/
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