39509

Автор(ы): 

Автор(ов): 

1

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

On some catigories of Monge-Ampère systems of equations

DOI: 

10.1070/SM2009v200n11ABEH004055

Наименование источника: 

  • Sbornik: Mathematics

Обозначение и номер тома: 

200:11

Город: 

  • Москва

Издательство: 

  • Springer PLEIADES PUBLISHING, МАИК " НАУКА/INTERPERIODICA"

Год издания: 

2009

Страницы: 

1681–1714
Аннотация
The paper looks at differential-geometric structures associated with Monge-Amp`ere systems of equations on manifolds and how they can be applied in the reduction of these equations. The category of Monge-Amp`ere systems of equations is investigated; its morphisms are changes of independent and dependent variables. Some subcategories of this category are also studied. The main emphasis is on subcategories of equations of locally equivalent triangular and semitriangular systems, systems that are linear with respect to derivatives (semilinear systems), systems with constant coefficients, and also complete differential systems. Tests, which can be verified effectively, are proved; these make it possible to establish whether a given system of Monge-Amp`ere equations belongs to the subcategories listed above. As corollaries, conditions for a Monge-Amp`ere system to be locally reducible to a single first- or second-order equation are obtained.

Библиографическая ссылка: 

Туницкий Д.В. On some catigories of Monge-Ampère systems of equations // Sbornik: Mathematics. 2009. 200:11. С. 1681–1714.

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