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

Авторы: Kosov A.A., Semenov E.I., Sinitsyn A.V.

Журнал: Publications de l’Institut Mathematique. Nouvelle série

Том: 98

Номер: 112

Год: 2015

Отчётный год: 2015

Издательство:

Местоположение издательства:

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Проекты:

DOI: 10.2298/PIM1512119K

Аннотация: 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.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет

Публикация в печати: 0