As. Fokas et C. Rogers, Initial/boundary value problems for simultaneous evolution equations in three dimensions, STUD APPL M, 107(4), 2001, pp. 391-401
A novel procedure recently introduced by the senior author is adapted here
for the analysis of initial/boundary value problems for pairs of linear dis
persive evolution equations in three dimensions. Such simultaneous equation
s are shown to arise naturally out of linear representations for 2+1-dimens
ional nonlinear integrable equations. The method presented emanates from th
e encoding of such simultaneous equations as the condition that a certain d
ifferential 1-form is closed.