Integrability conditions for differential systems
In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example, including Lax pairs of integrable systems. A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system. To elaborate, a Pfaffian system is a set of 1-forms on a smooth manifold (which one sets equal to 0 to find solutions to the system).
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Integrability conditions for differential systems
In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example, including Lax pairs of integrable systems. A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system. To elaborate, a Pfaffian system is a set of 1-forms on a smooth manifold (which one sets equal to 0 to find solutions to the system).
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In mathematics, certain system ...... f sufficiently high dimension.
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Równanie Pfaffa – typ równania ...... ska niemieckiego matematyka, .
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Пфа́ффово уравнение — уравнени ...... зываемой симметричной форме: .
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数学において、ある種の偏微分方程式系は、内在する幾何学的ない ...... 元で積分可能な部分多様体が存在することを保証する条件を言う。
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In mathematics, certain system ...... find solutions to the system).
@en
Równanie Pfaffa – typ równania ...... ska niemieckiego matematyka, .
@pl
Пфа́ффово уравнение — уравнени ...... зываемой симметричной форме: .
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数学において、ある種の偏微分方程式系は、内在する幾何学的ない ...... ⊂ M は埋め込まれた多様体である必要はないことに注意する。
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Integrability conditions for differential systems
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Równanie Pfaffa
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Пфаффово уравнение
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微分方程式系の可積分条件
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