Josephson junction with variable thickness of the dielectric layer.

The dynamics of the fluxon in the Josephson junction is studied. The dielectric layer of the junction has a variable thickness. It is shown that the modified area of the junction acts on the fluxon as a potential barrier. The relation between the critical bias current and the thickness of the dielectric layer is analytically and numerically determined.

Perturbation scheme for a fluxon in a curved Josephson junction.

The kink solution in the long Josephson junction is studied. The perturbation scheme of constructing the fluxon solution in curved junction is formulated. The prediction from the perturbation scheme is compared with the prediction that follows from the numerical studies of the complete field model.

Kink motion in a curved Josephson junction.

The propagation of the kink along the curved Josephson junction is considered. It is shown that the torsion as well as curvature is responsible for the existence of the energy barrier that affects the motion of the fluxon in the junction. It is also observed that the motion of the kink in the junction can be controlled in a very simple way even in the straight junction by modulating its width.

Construction of curved domain walls.

The evolution of the domain wall is reduced to the dynamics of the membrane. The rigorous construction of curved membranes in the real scalar field models with domain-wall solutions is presented. An example of the curved membrane is discussed in detail. The curved domain-wall solutions are constructed.

Defect production behind the shock wave front of an inhomogeneous quench.

The creation of defects behind the half kink in the presence of external force distributions is considered. The influence of external potentials on kink production behind the shock wave front of an inhomogeneous quench is examined. It is shown that depending on the impurity strength and orientation its interaction with the front of the decaying false vacuum, even in homogenous systems, may lead to single or even multiple defect production in the vicinity of the impurity center.

Kink production in the presence of random distributed impurities.

Production of kinks during a quench in an overdamped regime of phi(4) model is investigated. An influence of random distributed impurities on defect production is studied.

Kink production in the presence of impurities.

The production of kinks during a quench in an overdamped regime of phi(4) model is investigated. Expelling defects from regions of nonzero force coming from the impurity are predicted.

Kinks of arbitrary width.

The influence of external potentials on kink width is investigated. The stability of a single kink and kink-antikink solutions in the presence of an external force is proved. The consequences of stability for defect production during a quench are discussed.