Phonons, rotons and ripplons at interfaces

We use dispersive hydrodynamics to describe thermal excitations of superfluid helium 4. Dispersion relation of the bulk quasiparticles, phonons and rotons, acts as an input parameter of the theory. Wiener and Hopf method is used to solve nonlocal equations of the fluid in half-space. The dispersion relation helium surface excitations, ripplons, is derived and analyzed; numerical solution reveals its new unusual branch. The same method applies to the description of bulk quasiparticles' interaction with the interface with a solid. All quasiparticles creation probabilities are derived and weak interaction of rotons with negative dispersion with interfaces is explained.