  Nonlinear integrable models with two spatial and one temporal variables:
Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are
investigated on the subject of correct formulation for boundary problem that
can be solved within the framework of the Inverse Scattering Problem method. It
is shown that there exists a large set of integrable boundary problems and
various curves can be chosen as boundary contours for them. We develop a method
for obtaining explicit solutions to integrable boundary problems and its
effectiveness is illustrated by series of examples.
