Solitons and their resonances on two-dimensional superfluid films

Abstract

Abstract. The dynamics of sa'turated two-dimensional superfluid 4He films is shown to be gO,verned by the Kadomtsev-Petviashvili equation with negative dispersion. It is established that the phenomena of soliton resonance could be observed in such films. Under the .lowest order nonjinearity, such resonance would happen only if two dimensional effects arc taken into ,account. The amplitude and velocity of the resonant soliton are obtained.

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

“…Thus we can identify that in present case, In previous scientific literatures, the surface wave dynamics of saturated superfluid film has been considered in very few cases [6,15]. In [6] KdV equation was derived as surface wave evolution equation where thermomechanical force was neglected.…”

“…From (15), we see that ultimately we have got forced KP-I equation as the (2+1) dimensional evolution equation of free surface. It is known that all integrable equations possess soliton solutions which are exponentially localized solutions in certain directions.…”

“…We follow the method from [33] and proceed to find the solution of (15). In the first place, we consider C to be a rapidly varying function i.e, C = f(X,Y,T/ 1 ), where 0 < 1 << 1.…”

“…They also considered large amplitude density fluctuations in a thin superfluid film and discussed about existence of "quasi-solitons" under collision [14]. In [15] they showed the free surface dynamics of saturated two-dimensional superfluid 4 He film is governed by the KP equation. It is showed that soliton resonance could happen at lowest order nonlinearity, if two dimensional effects are considered.…”

“…We shall see that due to that effect the dynamics of the surface wave will be changed. We follow the derivation of [15] with nontrivial boundary conditions at the bottom.…”