  Inverse scattering transform method of the heat equation is developed for a
special subclass of potentials nondecaying at space infinity---perturbations of
the one-soliton potential by means of decaying two-dimensional functions.
Extended resolvent, Green's functions, and Jost solutions are introduced and
their properties are investigated in detail. The singularity structure of the
spectral data is given and then the Inverse problem is formulated in an exact
distributional sense.
