a2 Department of Mathematics, Yeshiva University, New York, NY 10033, USA (email@example.com)
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.
(Received July 16 2009)
(Accepted October 26 2009)