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Enhanced Symmetry Analysis of Two-Dimensional Burgers System

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Abstract

We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are comprehensively studied in the optimal way and new Lie invariant solutions are constructed. We prove that this system admits no local conservation laws and then study hidden conservation laws, including potential ones. Various kinds of hidden symmetries (continuous, discrete and potential ones) are considered for this system as well. We exhaustively describe the solution subsets of the Burgers system that are its common solutions with its inviscid counterpart and with the two-dimensional Navier–Stokes equations. Using the method of differential constraints, which is particularly efficient for the Burgers system, we construct a number of wide families of solutions of this system that are expressed in terms of solutions of the (\(1+1\))-dimensional linear heat equation although they are not related to the well-known linearizable solution subset of the Burgers system.

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Acknowledgements

R.O. Popovych and C. Sophocleous would like to express their gratitude for the reciprocal hospitality shown by their two institutions. The research of ROP was supported by the Austrian Science Fund (FWF), project P25064.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, Nicosia, CY 1678, Cyprus

    Stavros Kontogiorgis & Christodoulos Sophocleous

  2. Wolfgang Pauli Institut, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Roman O. Popovych

  3. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs’ka Str., 01004, Kyiv, Ukraine

    Roman O. Popovych

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  1. Stavros Kontogiorgis
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  2. Roman O. Popovych
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  3. Christodoulos Sophocleous
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Correspondence to Christodoulos Sophocleous.

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Kontogiorgis, S., Popovych, R.O. & Sophocleous, C. Enhanced Symmetry Analysis of Two-Dimensional Burgers System. Acta Appl Math 163, 91–128 (2019). https://doi.org/10.1007/s10440-018-0215-9

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