Hodge-Frobenius方程和Hodge-Backlund变换
Hodge-Frobenius equations and the Hodge-Backlund transformation
摘要：
研究了线性和非线性Hodge-like系统的1-形式，用完全可积的假设代替了外微分下的封闭性要求。系统被放置在变分的背景下，研究临界点的性质。能量密度的某些标准选择与使用霍奇对合的基本性质的贝克兰德变换有关。这些Hodge-Backlund变换产生在不同背景下出现的经典Backlund变换的不变形式。一些扩展到更高程度的形式表示。
英文摘要：
Linear and nonlinear Hodge-like systems for 1-forms are studied, with an assumption equivalent to complete integrability substituted for the requirement of closure under exterior differentiation. The systems are placed in a variational context and properties of critical points investigated. Certain standard choices of energy density are related by Backlund transformations which employ basic properties of the Hodge involution. These Hodge-Backlund transformations yield invariant forms of classical Backlund transformations that arise in diverse contexts. Some extensions to higher-degree forms are indicated.
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