Related papers: Dynamics of Lattice Kinks
In this paper we compute asymptotics of solutions of the kinetic Fokker-Planck equation with inelastic boundary conditions which indicate that the solutions are nonunique if $r < r_c$. The nonuniqueness is due to the fact that different…
We analyze the generation and mobility of discrete solitons in Bose-Einstein condensates confined in an optical lattice under realistic experimental conditions. We discuss first the creation of 1D discrete solitons, for both attractive and…
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying…
We conduct a comprehensive analysis of the large-space and long-time asymptotics of kink-soliton gases in the sine-Gordon (sG) equation, addressing an important open problem highlighted in the recent work [Phys. Rev. E 109 (2024) 061001].…
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink…
We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…
In this work, we investigate the solutions of vortices in the O(3)-sigma model with the gauge field governed by the Chern-Simons term and subject to a hyperbolic self-dual potential. We show that this model admits both topological and…
In this paper we study the Klein-Gordon (KG) lattice with periodic boundary conditions. It is an $N$ degrees of freedom Hamiltonian system with linear inter-site forces and nonlinear on-site potential, which here is taken to be of the…
We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices solitons centered on cubic domains may be stabilized even in…
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…
In this work, we investigate the dynamics of a scalar field in the nonintegrable $\displaystyle \phi ^{4}$ model, restricted to the half-line. Here we consider singular solutions that interpolate the Dirichlet boundary condition…
We investigate the interface coupling between the 2D sine-Gordon equation and the 2D wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the…
The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a…
We consider an extended model with two real scalar fields, $\phi(x,t)$ and $\chi(x,t)$. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the $\chi^4$ one. The fields mutually interact…
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…
Evolution of sphalerons in a class of quartic Klein-Gordon models are studied under a growing perturbation. Sphalerons are unstable lump-like solutions that arise from a saddle point between true and false vacua in the energy functional.…
In an attempt to understand the soliton resolution conjecture, we consider the Sine-Gordon equation on a spherically symmetric wormhole spacetime. We show that within each topological sector (indexed by a positive integer degree $n$) there…
The sine-Gordon model is studied with model parameters that depend on both space and time. An effective model with one degree of freedom is constructed, allowing the description of the kink movement in both a temporally non-autonomous and…
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 consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is…