ISSN 2658–5782
DOI 10.21662
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Babkov O.K., Mukhametova G.Z. Group classification of third order nonlinear wave equations chain’s. Multiphase Systems. 15 (2020) 3–4. 232–237 (in Russian).
2020. Vol. 15. Issue 3–4, Pp. 232–237
URL: http://mfs.uimech.org/mfs2020.3.136
DOI: 10.21662/mfs2020.3.136
Group classification of third order nonlinear wave equations chain’s
Babkov O.K., Mukhametova G.Z.
Ufa State Aviation Technical University, Ufa, Russia

Abstract

The paper presents the results of point symmetrys Lie algebras for third-order nonlinear wave equations calculating linked into a chain by Bäcklund transformations. Calculations are carried out by using Lie-Ovsyannikov method of group analysis. The basic algebras of point symmetries of the indicated equations are found, all possible cases of their extension are revealed, and the commutator tables of algebras found are calculated.

Keywords

differential equations’s chain,
group classification,
admissible operator,
Lie algebra,
commutators table

References

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  2. Ovsyannikov L.V. [Lectures on the theory of group properties of differential equations] Lekcii po teorii guppovyx svojstv differencial’nyx uravnenij. Novosibirsk: NSU, 1966. 132 p.
  3. Ibragimov N.H. [Transformation groups in mathematical physics] Gruppy preobrazovanij v matematicheskoj fizike. M.: Science, 1983. 280 p.
  4. Ibragimov N.H. CRC Handbook of Lie group analysis of differential equations. Vol. 1: Symmetries, exact solutions and conservation laws. Boca Ration: CRC Press Inc., 1994.