The thesis is dedicated to investigating interaction of a quantum fluid's quasiparticles with the interface with a solid - their reflection, transmission and creation on the interface by each other or by the solid's phonons. In the thesis the theory of a quantum fluid as continuous medium at all length scales is proposed, in which it is treated as a continuous medium with correlations on interatomic distances. The nonlocality of this theory enables one to consider a quantum fluid with arbitrary nonlinear dispersion relation. The quasiparticles of a quantum fluid are described as wave packets propagating in the medium. Thus the approach provides, in particular, a unified model for all the quasiparticles of superfuid helium - phonons, R-rotons and R+rotons, which belong to the same nonmonotonic dispersion curve. R-rotons correspond to the decreasing segment and have negative dispersion. The equations of quantum fluid as a continuous medium with correlations in half-space are solved in the general case. It is shown, that divergence of the dispersion relation from the linear one leads to existence of special boundary waves in the solution. The problem of quasiparticles' interaction with the interface is solved for the first time for the case of essentially nonlinear but monotonic dispersion relation of Bose-Einstein condensate. It is shown, that the boundary waves, that enter the solution due to the nonlinearity, alter the values of variables of continuous medium at the interface, thus changing the reflection and transmission coefficients for the wave packets. The amplitude reflection and transmission coefficients are derived. They are complex quantities, which means that there are nontrivial phase shifts between the incident, reflected and transmitted waves. The energy coefficients are derived taking into account that in a wave packet the energy is transferred with group velocity. At small frequencies the considered dispersion relation approximates the anomalous dispersion relation of superfluid helium, so inthis limit the correction to the transmission coefficient through the interface between superfluid helium and a solid is derived. The frequency dependences of the coefficients and transmission angles lead to the effects of wave packets deformation on reflection and transmission through the interface, which are also investigated. The problem of interaction of superfluid helium phonons, R-rotons and R+rotons with the interface is solved. The set of six critical angles are introduced. These separate the intervals of incidence angles for the different quasiparticles, for which other quasiparticles can be created. The effect of retro-reflection is predicted for the processes with creation or destruction of R-rotons. The probabilities of all quasiparticles creation on the interface on the incidence of each of them are derived as functions of frequency and incidence angles. It is shown that the creation probability of an R-roton by a solid's phonon and vice versa are very small for all angles and frequencies. This means that R-rotons are both badly created by a solid heater and poorly they are detected by a solid bolometer. Thus the explanation is given to the failures in detection of R-rotons in the early direct experiments, in which these instruments were used. New predictions are made on experiments on interactions of beams of phonons and rotons with the solid interface and creation of R-rotons on the interface by a beam of high-energy phonons. The individual contributions of helium phonons, R-rotons, and R+rotons into the full energy flow through the interface are calculated at thermodynamic equilibrium, as well as the contribution to the Kapitza temperature jump. The R-rotons' parts are shown to be very small. The pressure of the quasiparticles gas on the interface is derived as well as the individual contributions to it of phonons', R-rotons', and R+rotons' parts of the dispersion curve. The pressure due to the R-rotons is shown to be negative due to their negative group velocity. It is compensated by the positivepressure due to R+rotons, and the total roton pressure is positive and is several times less than the absolute value of either the R+ or R-roton contribution. The partial pressures of quasiparticles of different types can be expressed in the form of the pressure of a classical gas, despite the fact that quasiparticles interact with the interface in a much more complex manner. This result should hold true for any two adjacent continuous media. One of the consequences is that the net force, which the quasiparticles of both media exert on the interface, is directed towards the medium with the greater sound velocity of the two. It is shown that the expression derived for pressure, due to phonons, R- and R+rotons, is the same as the fountain pressure in helium. So the fountain effect is due to the osmotic pressure of the quasiparticles that are "solvated" in the superfluid. The negativeness of the R-rotons' pressure but with the obvious positiveness of their contribution to the entropy of superfluid helium, is explained. An experiment is suggested for detecting the negative momentum transferred to a membrane by an incident R-roton beam, which is created by mode change reflection of high-energy phonons at an interface with a solid
