Group and renormgroup symmetry of quasi-Chaplygin media. (English) Zbl 0951.35115
In the paper the results of renormgroup analysis of a quasi-Chaplygin system of equations are presented. The Lie-Bäcklund symmetries and corresponding invariant solutions for different “Chaplygin” functions are obtained. The algorithm for the construction of a group on a solution (renormgroup) using two different approaches is discussed.
Reviewer: L. N. Chernetskaja (Kyïv)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Software:
DIMSYMReferences:
| [1] | Chaplygin, SA, On gas jets, 1949, Moscow-Leningrad: GITTL, Moscow-Leningrad |
| [2] | Trubnikov, BA; Zhdanov, SK, Quasi-Gaseous Unstable Media, 1991, Moscow: Nauka Publishers, Moscow |
| [3] | CRC Handbook of Lie Group Analysis of Differential Equations, V.1, Symmetries, Exact Solutions and Conservation Laws, ed. by N.H. Ibragimov CRC Press, Boca Raton, Florida, USA, 1994. · Zbl 0864.35001 |
| [4] | Ovsyannikov L.V., Group Properties of Differential Equations, Izdat Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk, 1962, p.136. |
| [5] | Kovalev, VF; Pustovalov, VV; Senashov, SI, Differential Equations, 29, 1521, 1993 · Zbl 0836.35151 |
| [6] | Pustovalov V.V. and Shvarev A.K., Group and Renormgroup Analysis of Nonlinear Geometrical Optics Equations, 1. Lie symmetry, P.N. Lebedev Physical Institute, Preprint N 15, April 1994. |
| [7] | Sheftel, MB, Vestnik LGU, 56, 368, 1983 |
| [8] | Sherring J. and Prince G., DIMSYM - Symmetry Determination and Linear Differential Equations Package, Department of Mathematics, La Trobe University, Melbourne, Australia, preprint 1992. · Zbl 0770.58035 |
| [9] | Akhmanov, SA; Khokhlov, RV; Sukhorukov, AP, ZhETF, 50, 1537, 1966 |
| [10] | Kovalev V.F. and Pustovalov V.V., Quasi-Chaplygin Media Equations: Theoretical Group Approach, Institute for Mathematical Modelling, Preprint N 14, 1994. |
| [11] | Shirkov, DV, Usp. Matem. Nauk, 49, 147-164, 1994 · Zbl 0849.46057 |
| [12] | Kovalev V.F. and Pustovalov V.V., Lie Groups and their Applications, 1994, V.1, N 2, 104 (Celal Bayar University, Manisa, Turkey). · Zbl 0938.35599 |
| [13] | Kovalev V.F., Krivenko S.V. and Pustovalov V.V., Lie Symmetry and a Group on a Solution of a Boundary-Value Problem, P.N.Lebedev Physical Institute, Preprint N 13, April 1995. |
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