Abstract:
We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).

Abstract:
We show how detailed properties of a kink in quantum field theory can be extracted from field correlation functions. This makes it possible to study quantum kinks in a fully non-perturbative way using Monte Carlo simulations. We demonstrate this by calculating the kink mass as well as the spectrum and approximate wave functions of its excitations. This way of measuring the kink mass has clear advantages over the existing approaches based on creation and annihilation operators or the kink free energy. Our methods are straightforward to generalise to more realistic theories and other defect types.

Abstract:
The motion of a one-dimensional kink and its energy losses are considered as a model of interaction of nontrivial topological field configurations with external fields.

Abstract:
We predict theoretically that surface of an optical lattice imprinted in defocusing nonlinear media can support shock, or kink waves. Such new surface waves contain a modulationally stable pedestal and are strongly localized at the edge of the optical lattice due to Bragg-type reflection. The kink steepness and localization degree can be controlled by the lattice depth. We found two types of kinks, which exhibit distinct stability properties for each finite gap in the lattice spectrum. Our findings open the way to experimental observation of optical surface kink waves.

Abstract:
By allowing the light cones to tip over on hypersurfaces according to the conservation laws of an one-kink in static, Schwarzschild black hole metric, we show that in the quantum regime there also exist instantons whose finite imaginary action gives the probability of occurrence of the kink metric corresponding to single chargeless, nonrotating black hole taking place in pairs, the holes of each pair being joined on an interior surface, beyond the horizon.

Abstract:
The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.

Abstract:
There are several two dimensional quantum field theory models which are equipped with different vacuum states. For example the Sine-Gordon- and the $\phi^4_2$-model. It is known that in these models there are also states, called soliton- or kink-states, which interpolate different vacua. We consider the following question: Which are the properties a pair of vacuum sates must have, such that an interpolating kink-state can be constructed? Since we are interested in structural aspects and not in specific details of a given model, we are going to discuss this question in the framework of algebraic quantum field theory which includes, for example, the $P(\phi)_2$-models. We have shown that for a large class of vacuum states, including the vacua of the $P(\phi)_2$-models, there is a natural way to construct an interpolating kink-state.