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 are investigated. Certain standard choices of energy density are related by B¨acklund transformations which employ basic properties of the Hodge involution. These Hodge–B¨acklund transformations yield invariant forms of classical B¨acklund transformations that arise in diverse contexts. Some extensions to higher-degree forms are indicated.
Hodge-Frobenius equations and the Hodge-Backlund transformation
MARINI, ANTONELLA;
2010-01-01
Abstract
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 are investigated. Certain standard choices of energy density are related by B¨acklund transformations which employ basic properties of the Hodge involution. These Hodge–B¨acklund transformations yield invariant forms of classical B¨acklund transformations that arise in diverse contexts. Some extensions to higher-degree forms are indicated.File in questo prodotto:
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