In this thesis the following problems on properties of solid ⁴He are considered: (i) the role of long-range interactions in suppression of dislocation roughening at T = 0; (ii) the combined effect of ³He impurities and Peierls potential on shear modulus softening; (iii) the dislocation superclimb and its connection to the phenomenon of ”giant isochoric compressibility”; (iv) non-linear dislocation response to the applied stress and stress-induces dislocation roughening as a I-order phase transition in 1D at finite temperature.

First we investigate the effect of long-range interactions on the state of edge dislocation at T = 0. Such interactions are induced by elastic forces of the solid. We found that quantum roughening transition of a dislocation at T = 0 is completely suppressed by arbitrarily small long-range interactions between kinks. A heuristic argument is presented and the result has been verified by numerical Monte-Carlo simulations using Worm Algorithm in J-current model.

It was shown that the Peierls potential plays a crucial role in explaining the elastic properties of dislocations, namely shear modulus softening phenomenon. The crossover from T = 0 to finite temperatures leads to intrinsic softening of the shear modulus and is solely controlled by kink typical energy. It was demonstrated that the mechanism, involving only the binding of ³He impurities to the dislocations, requires an unrealistically high concentrations of defects (or impurities) in order to explain the shear modulus phenomenon and therefore an inclusion of Peierls potential in consideration is required.

Superclimbing dislocations, that is the edge dislocations with the superfluidity along the core, were investigated. The theoretical prediction that superclimb is responsible for the phenomenon of "giant isochoric compressibility" was confirmed by Monte-Carlo simulations. It was demonstrated that the isochoric compressibility is suppressed at low temperatures. The dependence of compressibility on the dislocation length was shown to be strongly dependent on long-range interaction.

Non-linear behavior at high stresses was considered. The dislocation was observed to exhibit two types of behavior depending on the dislocation size: reversible and hysteretic. In the reversible regime responses of superclimbing dislocations exhibit sharp resonant peaks. We attribute this feature to the resonant creation of jog-antijog pairs. The peak in the compressibility results in the dip in the speed of sound which we believe was observed in ”UMASS-sandwich” mass-transport experiments. The hysteresis revealed an unusually strong sensitivity to the dislocation size signifying that the stress-induced roughening is a I-order phase transition in 1D at finite T.