Related papers: Topological discrete kinks
The study of kink interactions in nonlinear Klein-Gordon models in $1+1$-dimensions has a time-honored history. Until a few years ago, it was arguably considered a fairly mature field whose main phenomenology was well understood both…
In both the Gardner equation and its extensions, the non-convex convection bounds the range of solitons / compactons velocities beyond which they dissolve and kink/anti-kink form. Close to solitons barrier we unfold a narrow strip of…
This study explores the scattering dynamics of kinks within a nonlinear system governed by a parameterized potential $U_\lambda(\chi)$, examining the distinct behaviors of small and large kinks across a range of $\lambda$ values and initial…
We prove the existence of periodic travelling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases of hard and soft on-site potentials. In the case of hard on-site potentials we implement a fixed point…
In this paper we study global nonlinear stability for the Dirac-Klein-Gordon system in two and three space dimensions for small and regular initial data. In the case of two space dimensions, we consider the Dirac-Klein-Gordon system with a…
We prove global well-posedness below the charge norm (i.e., the $L^2$ norm of the Dirac spinor) for the Dirac-Klein-Gordon system of equations (DKG) in one space dimension. Adapting a method due to Bourgain, we split off the high frequency…
We propose a system of sine-Gordon equations, with the $\mathcal{PT}$ symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from…
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of…
We present a geometric extension of the Bogomolny-Prasad-Sommerfield (BPS) construction for scalar kinks in (1+1) dimensions embedded in static curved spacetimes. By introducing a nonminimal coupling between the scalar prepotential and the…
In this paper, we present topological defects in $(1,1)$ dimensions, described by an extended nonlinear $O(3)$ sigma model. We consider spherical coordinates $(\phi,\chi)$ in the $S^2$ isotopic space and a potential $V(\phi,\chi)$. For…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
We consider the Klein-Gordon system posed in an inhomogeneous medium with smooth boundary subject to a local viscoelastic damping distributed around a neighborhoodof the boundary according to the Geometric Control Condition. We show that…
We have found exact, periodic, time-dependent solitary wave solutions of a discrete $\phi^4$ field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi…
We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations…
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 study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities.…
To show that steadily propagating nonlinear waves in active matter can be driven internally, we develop a prototypical model of a topological kink moving with a constant supersonic speed. We use a model of a bi-stable mass-spring (FPU)…
A chain of interacting particles subject also to a nonlinear on-site potential admits stable soliton-like configurations : static kinks. The linear normal-modes around such a kink contain a discrete set of localized, gap-separated modes.…
In this paper, we investigate the almost-periodic solutions for the one-dimensional nonlinear Klein-Gordon equation within the non-relativistic limit under periodic boundary conditions. Specifically, by employing the method introduced in…
The Peierls-Nabarro barrier is a discrete effect that frequently occurs in discrete nonlinear systems. A signature of the barrier is the slowing and eventual stopping of discrete solitary waves. This work examines intense electromagnetic…