American Institute of Mathematical Sciences

December  2014, 7(6): 1165-1179. doi: 10.3934/dcdss.2014.7.1165

Connections of zero curvature and applications to nonlinear partial differential equations

 1 Department of Mathematics, University of Texas, Edinburg, TX, 78540, United States

Received  January 2013 Revised  September 2013 Published  June 2014

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.
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
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