This article is cited in 2 papers

Integrable models of magnetic insulation and their exact radially symmetric solutions

A. A. Kosov^a, E. I. Semenov^a, A. V. Sinitsyn<sup>b

a</sup> Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences (ISDCT SB RAS)
^b Universidad Nacional de Colombia, Bogota, Colombia

Abstract: A singular boundary value problem for the model of vacuum diode is studied. Integrability of the system of nonlinear differential equations is justified and a complete system of the first integrals is constructed. A method of solving singular boundary value problem is developed. The generalized model with Laplace's three-dimensional operator is offered. For the generalized model parametrical families of exact solutions are constructed.

Keywords: first integrals, integrability, singular boundary value problem, equations of elliptic type, exact solutions, vacuum diode.

UDC: 519.946