Initial/boundary value problems for simultaneous evolution equations in three dimensions

A novel procedure recently introduced by the senior author is adapted here for the analysis of initial/boundary value problems for pairs of linear dispersive evolution equations in three dimensions. Such simultaneous equations are shown to arise naturally out of linear representations for 2+1-dimensional nonlinear integrable equations. The method presented emanates from the encoding of such simultaneous equations as the condition that a certain differential 1-form is closed.