The escape problem in a classical field theory with two coupled fields

We introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to not only model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems.