Connections of zero curvature and applications to nonlinear partial differential equations

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

12-2014

Abstract

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Bäcklund tranformations can be formulated for such equations that occur as zero curvature terms.

Comments

Original published version available at doi.org/10.3934/dcdss.2014.7.1165

Recommended Citation

Paul Bracken. Connections of zero curvature and applications to nonlinear partial differential equations. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1165-1179. doi: 10.3934/dcdss.2014.7.1165

Publication Title

Discrete and Continuous Dynamical Systems - Series S

DOI

10.3934/dcdss.2014.7.1165