Free surface lump wave dynamics of a saturated superfluid ⁴ He film with nontrivial boundary condition at the substrate surface

Abstract

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

Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO) plasma region

“…The complete solution of forced KPII equation 29 can be obtained by substituting these perturbative solutions at different orders in equation 59. This kind of perturbative solution is also discussed by Mukherjee [20] recently in the context of forced KPI equation. Substituting different types of space time dependent localized forcing functions like Gaussian, hyperbolic etc.…”

“…For dealing with this kind of special spatially independent, and only temporally dependent forcing function, we follow closely the recent work by Mukherjee [20]. It is found that the forced KPII equation becomes exactly solvable for this special kind of forcing.…”