Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 2010 - Volume 140, Issue 04  

Research Article

Hodge-Frobenius equations and the Hodge–Bäcklund transformation

Antonella Marinia1 and Thomas H. Otwaya2

a1 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)

a2 Department of Mathematics, Yeshiva University, New York, NY 10033, USA (otway@yu.edu)

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.

(Received July 16 2009)

(Accepted October 26 2009)