Author:
Marini Antonella,Otway Thomas H.
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.
Publisher
Cambridge University Press (CUP)
Cited by
7 articles.
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1. Strong solutions to a class of boundary value problems on a mixed Riemannian--Lorentzian metric;Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain);2015-11
2. Bäcklund Transformations and Hodge-Theoretic Methods;SpringerBriefs in Mathematics;2015
3. Introduction;SpringerBriefs in Mathematics;2015
4. Duality methods for a class of quasilinear systems;Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire;2014-04
5. Constructing completely integrable fields by a generalized-streamlines method;Communications in Information and Systems;2013