Related papers: Topological discrete kinks

We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear…

We show that in a special type of two-dimensional dilaton-gravity-scalar model, where both the dilaton and the scalar matter fields have noncanonical kinetic terms, it is possible to construct kink solutions whose linear perturbation…

We consider a finite but arbitrarily large Klein-Gordon chain, with periodic boundary conditions. In the limit of small couplings in the nearest neighbor interaction, and small (total or specific) energy, a high order resonant normal form…

It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with…

When a self-localized quasiparticle excitation propagates along a discrete one dimensional lattice, it becomes subject to a dissipation that converts the kinetic energy into lattice vibrations. Eventually the kinetic energy does no longer…

We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is non-homogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which…

In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential…

The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…

We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional…

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…

Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equation. The disparity between the two forms is the discretization…

In recent years, three exceptional discretizations of the phi^4 theory have been discovered [J.M. Speight and R.S. Ward, Nonlinearity 7, 475 (1994); C.M. Bender and A. Tovbis, J. Math. Phys. 38, 3700 (1997); P.G. Kevrekidis, Physica D 183,…

We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial bandstructure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a non-trivial…

We prove that the Cauchy problem for the Dirac-Klein-Gordon system of equations in 1+3 dimensions is locally well-posed in a range of Sobolev spaces for the Dirac spinor and the meson field. The result contains and extends the earlier known…

The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave…

We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic, asymmetric lattice of point-like inhomogeneities. We explain the underlying rectification mechanism within a collective coordinate framework, which shows…

In this article, we study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we…

Nonlinearity induced topological properties in nonlinear lattice systems are studied in both momentum space and real space. Experimentally realizable through the Kerr effect on photonic waveguide systems, our working model depicts on-site…

The two major effects observed in collisions of the continuum $\phi^4$ kinks are (i) the existence of critical collision velocity above which the kinks always emerge from the collision and (ii) the existence of the escape windows for…

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…