On the analytical properties and some exact solutions of the Glukhovsky-Dolzhansky system

Abstract

Non-linear dynamical systems describe many physical processes. In this work we investigate a three-dimensional Lorenz-like system - the Glukhovsky-Dolzhansky system. We consider analytical properties of the studied system. The problem of existence of meromorphic solution is discussed. We perform the Painlevè test and find conditions imposed on parameters of the system for which meromorphic solutions exist. Laurent series locally representing solutions are built. First integrals are obtained. We also find simply periodic solutions with one and two poles in a stripe of periods.