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 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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