Related papers: Solitons: Kinks, Collisions and Breathers
Guided by a study of kink-antikink scattering in the Gross-Neveu model and other known solutions of the Hartree-Fock approach of a particularly simple type, we demonstrate a quantitative relationship between three different problems:…
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on…
We study various properties of topological solitons (kinks) of a field-theoretic model with a polynomial potential of the twelfth degree. This model is remarkable in that it has several topological sectors, in which kinks have different…
We study the soliton type solutions arising in two-dimensional quantum chromodynamics (QCD$_{2}$). The so-called generalized sine-Gordon model (GSG) arises as the low-energy effective action of bosonized QCD$_{2}$ for unequal quark mass…
We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein-Gordon models. The multi-kinks are constructed using Lin's…
These lectures deal mainly with solitons in three-dimensional Moyal-deformed sigma models. The topics are: static and moving (multi-)solitons of the (integrable) Ward sigma model, with space-space and time-space noncommutativity, their…
The sine-Gordon equation on a metric graph with a structure represented by a $\mathcal{Y}$-junction, is considered. The model is endowed with boundary conditions at the graph-vertex of $\delta'$-interaction type, expressing continuity of…
The bipartite ground state entanglement in a finite linear harmonic chain of particles is numerically investigated. The particles are subjected to an external on-site periodic potential belonging to a family parametrized by the unit…
An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the…
We modify the recently proposed model of Speight and Ward to make it possess time dependent solutions. We find that for each lattice spacing and for each velocity of the sine Gordon kink we can find a modification of the model for which…
We prove the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied.
The aim of this work is to establish a linear instability result of stationary, kink and kink/anti-kink soliton profile solutions for the sine-Gordon equation on a metric graph with a structure represented by a $\mathcal Y$-junction. The…
Evolution of the nonequilibrium inhomogeneities and topological defects is studied in terms of complex kink solutions of the sine-Gordon equation. The weakly damped oscillation of the sine-Gordon kink, named as the kink quasimode, is…
This work studies the dynamics of solutions to the sine-Gordon equation posed on a tadpole graph $G$ and endowed with boundary conditions at the vertex of $\delta$-type. The latter generalize conditions of Neumann-Kirchhoff type. The…
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum…
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…
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…
We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and…
We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations…