📝 SummarXiv

Abstract

We have formulated a novel quantum nonlinear Schrodinger equation describing of superfluid He4 in films at low temperatures. It is shown that in classical limit the found nonlinear Schrodinger equation reduces to a system of equations which are equivalent to Boussinesq equations describing the propagation of long gravity waves in incompressible fluids. This nonlinear Schrodinger equation leads to phonon-roton dispersion relation for elementary excitations in superfluid He4 films at low temperatures. The quartic soliton, dark soliton, cosine and elliptic periodic wave solutions are obtained analytically as weakly excited quantum waves propagating in He4 films. We have also shown numerically that the presented nonlinear Schrodinger equation describes the quartic and dark solitary waves in helium films. These solitary and periodic quantum waves can find numerous important practical applications.