EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 119–135 (2015)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home

EMIS Home

Pick a mirror

 		 

First integrals and exact solutions of the generalized models of magnetic insulation

Alexander Kosov, Edward Semenov, Alexander Sinitsyn

Institute of System Dynamics and Control Theory of SB RAS, Irkutsk, Russia; Universidad Nacional de Colombia, Bogota, Colombia

Abstract: We suggest generalizations of the mathematical model of magnetic insulation, described by multidimensional quasi potential ODE system or PDE system with two-dimensional Laplace operator. Existence conditions of the first integrals of a certain type for the class of nonlinear quasi potential systems, including the model vacuum diode are obtained. Integrability of the vacuum diode models is justified. We find for PDE system the class of exact radially symmetric solutions given by fractional-rational functions. The class of systems with variable density, reduced to a similar system with the constant current density by special transformations is specified. The class of exact solutions of the non-singular boundary-value problem in annular domain is found.

Keywords: unsolved systems; first integrals; integrability; elliptic equations; boundary-value problem; exact solutions

Classification (MSC2000): 34B09; 34B15; 34B60

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
© 2015–2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition