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

[摘要] 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.

[发布机构] Department of Applied Maths, NRNU MEPhI, 31 Kashirskoe shosse, Moscow; 115409, Russia^1

[效力级别] 数学

[关键词] Analytical properties;Exact solution;First integral;Laurent series;Lorenz-like systems;Meromorphic solutions;Periodic solution;Physical process