Local Decomposition and Accessibility of Nonlinear Infinite-Dimensional Systems

Abstract

This article deals with the local system decomposition of infinite-dimensional systems, which are described by second-order nonlinear partial differential equations. We show that if there exists a certain codistribution which is invariant under the generalized system vector field, a local triangular decomposition can be obtained. Furthermore, we draw connections to a different approach which is based on transformation groups. Throughout the article we apply differential geometric methods, highlighting the geometric picture behind the system description. The article is closed with a nonlinear example.