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

Abstract

In this article, the free surface dynamics of saturated (∼ 10 −6 cm) superfluid 4 He film is considered under the condition that there exists a very weak downward superfluid flow velocity into the substrate. For saturated film, the effect of surface tension plays a decisive role in the dynamics of the system. The free surface is shown to be governed by forced Kadomtsev Petviashvili-I equation, with the forcing function depending on downward superfluid velocity in the substrate. Exact and perturbative lump solutions of the (2+1) dimensional evolution equation are obtained and the effect of leakage velocity function on the lump solutions are shown.