  Dromions are exponentially localised coherent structures supported by
nonlinear integrable evolution equations in two spatial dimensions.In the study
of initial-value problems on the plane, such solutions occur only if one
imposes nontrivial boundary conditions at infinity, a situation of dubious
physical significance. However it is established here that dromions appear
naturally in the study of boundary-value problems. In particular, it is shown
that the long time asymptotics of the solution of the Davey-Stewartson I
equation in the quarter plane with arbitrary initial conditions and with zero
Dirichlet boundary conditions is dominated by dromions. The case of non-zero
Dirichlet boundary conditions is also discussed.
