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

First integrals and exact solutions of the generalized models of magnetic insulationAlexander Kosov, Edward Semenov, Alexander SinitsynInstitute of System Dynamics and Control Theory of SB RAS, Irkutsk, Russia; Universidad Nacional de Colombia, Bogota, ColombiaAbstract: We suggest generalizations of the mathematical model of magnetic insulation, described by multidimensional quasi potential ODE system or PDE system with twodimensional 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 fractionalrational 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 nonsingular boundaryvalue problem in annular domain is found. Keywords: unsolved systems; first integrals; integrability; elliptic equations; boundaryvalue 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.
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