Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2016

Идентификатор DOI: 10.1134/S0040577916110052

Ключевые слова: compatibility of differential equations, reduction, infinite-dimensional manifold, Grobner basis

Аннотация: We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Grobner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

Журнал: THEORETICAL AND MATHEMATICAL PHYSICS

Выпуск журнала: Vol. 189, Is. 2

Номера страниц: 1592-1608

ISSN журнала: 00405779

Место издания: NEW YORK

Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER

• Kaptsov O.V. (RAS, Siberian Branch, Inst Computat Modeling, Krasnoyarsk, Russia; Siberian Fed Univ, Krasnoyarsk, Russia)

• Web of Science Core Collection
• Scopus