Geodesic
Integrable models of magnetic insulation and their exact radially symmetric solutions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 45-56

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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, vacuum diode.
Mots-clés : equations of elliptic type, exact solutions 
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     title = {Integrable models of magnetic insulation and their exact radially symmetric solutions},
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A. A. Kosov; E. I. Semenov; A. V. Sinitsyn. Integrable models of magnetic insulation and their exact radially symmetric solutions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 45-56. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a4/