Aksenov A., Druzhkov K. Group classification and conservation laws of the system of equations of two-dimensional shallow water over uneven bottom (abstract)

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Speaker: Alexander Aksenov

Title: Group classification and conservation laws of the system of equations of two-dimensional shallow water over uneven bottom

Abstract:
A system of equations of two-dimensional shallow water over uneven bottom is considered. Overdetermined systems of equations for determining the symmetries and the conservation laws are obtained. The compatibilities of this overdetermined systems of equations are investigated. Symmetry operators and conservation laws are found. The results of the group classification have indicated that the system of equations of two-dimensional shallow water over uneven bottom cannot be linearized by point transformation in contrast to the system of equations of one-dimensional shallow water in the cases of horizontal and inclined bottom profiles.

Joint work with Konstantin Druzhkov.


Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.