Abstract
We study the system of nonlinear differential equations which expresses the constancy of the algebraic invariants of the Jacobian matrix for smooth vector fields in three-dimensional space. This system is equivalent to the equations of gas dynamics which describe the barochronous motions of a gas (the pressure and density depend only on the time). We present the results of computation of the admissible local Lie group and construction of the general solution of the system. We mention a few new problems that arise here.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chupakhin A. P., "On the barochronous motions of a gas," Dokl. Akad. Nauk, 352, No. 5, 624–626 (1997).
Ovsyannikov L. V., Group Analysis of Diffirential Equations [in Russian], Nauka, Moscow (1978).
Ovsyannikov L. V., "Isobaric motions of a gas," Differentsial'nye Uravneniya, 30, No. 10, 1792–1799 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ovsyannikov, L.V. Symmetry of the Barochronous Motions of a Gas. Siberian Mathematical Journal 44, 857–866 (2003). https://doi.org/10.1023/A:1025945021678
Issue Date:
DOI: https://doi.org/10.1023/A:1025945021678