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Hodge-Frobenius equations and the Hodge–Bäcklund transformation

Published online by Cambridge University Press:  04 August 2010

Antonella Marini  and
Thomas H. Otway
Antonella Marini
Affiliation:
Dipartimento di Matematica, Università di L'Aquila, 67100 L'Aquila, Italy (marini@dm.univaq.it) and Department of Mathematics, Yeshiva University, New York, NY 10033, USA (marini@yu.edu)
Thomas H. Otway
Affiliation:
Department of Mathematics, Yeshiva University, New York, NY 10033, USA (otway@yu.edu)
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 4 , August 2010 , pp. 787 - 819
Copyright
Copyright © Royal Society of Edinburgh 2010

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