On the solutions of a system of three differential equations with quadratic nonlinearities. (Russian) Zbl 0727.34008
Systems of three differential equations with quadratic nonlinearities in particular cases are reduced to the Lorenz system of convective motion. In this paper an analytic investigation of such systems is made by Painlevé analysis, and conditions for the existence and a method for the construction of exact solutions are given. The exact solutions are expressed by the solutions of the second and third Painlevé equations.
Reviewer: V.N.Gusyatnikova (Pereslavl-Zalessky)
MSC:
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
