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In this article, the free surface wave dynamics of a saturated superfluidHelium film is considered under the condition that there exists a very weakdownward localized superfluid flow into the substrate. For saturated film, theeffect of surface tension plays a decisive role in the surface wave evolutiondynamics of the system. The free surface evolution is shown to be governed byforced Kadomtsev Petviashvili-I equation, with the forcing function dependingon downward superfluid velocity at the substrate surface. Exact as well asperturbative free surface lump wave solutions of the (2+1) dimensionalnonlinear evolution equation are obtained and the effect of the leakagevelocity function on the lump wave solutions are shown.

Free surface lump wave dynamics of a saturated superfluid Helium film with nontrivial boundary condition at the substrate surface