https://doi.org/10.1140/epjp/s13360-021-01688-2
Regular Article
Dispersionless Davey–Stewartson system: Lie symmetry algebra, symmetry group and exact solutions
Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, 34469, Istanbul, Turkey
b
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Received:
22
March
2021
Accepted:
21
June
2021
Published online:
5
July
2021
Abstract
Lie symmetry algebra of the dispersionless Davey–Stewartson (dDS) system is shown to be infinite dimensional. The structure of the algebra turns out to be Kac–Moody–Virasoro one, which is typical for integrable evolution equations in 
dimensions. Symmetry group transformations are constructed using a direct (global) approach. They are split into both connected and discrete ones. Several exact solutions are obtained as an application of the symmetry properties.
In memory of Prof. Pavel Winternitz: A great mentor, collaborator and friend.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
