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 Bäcklund transformations which employ basic properties of the Hodge involution. These Hodge-Bäcklund transformations yield invariant forms of classical Bäcklund transformations that arise in diverse contexts. Some extensions to higher-degree forms are indicated.

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