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Lie symmetries of two-dimensional shallow water equations with variable bottom topography. (English) Zbl 1445.35279
Summary: We carry out the group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The equivalence group of this class is found by the algebraic method. Using algebraic techniques, we construct additional point equivalences between some of the listed cases of Lie-symmetry extensions, which are inequivalent up to transformations from the equivalence group.
©2020 American Institute of Physics
MSC:
35Q35 PDEs in connection with fluid mechanics
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
76U60 Geophysical flows
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MOST
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