Integration of the Korteweg-de Vries equation with a source

It is shown that solutions of the Korteweg-de Vries equation with a source which are rapidly decreasing as x to +or- infinity can be obtained by the inverse scattering method for the one-dimensional Schrodinger operator on a straight line. The conditions are found under which the Korteweg-de Vries equation with a source has a pure soliton solution. The results obtained are relevant to some problems in hydrodynamics, plasma physics, solid state physics, etc.