Related papers: Moving lattice kinks and pulses: an inverse method
We analyze the interaction of lattice vibrations (phonon wave-packets) with an asymmetric kink soliton initially at rest. We employ the $\phi^6$ model in one space and one time dimensions for various lattice spacings and consider two…
We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
We introduce the concept of soliton solutions of integrable nonlinear partial differential equations and point out that the inverse spectral method represents the rigorous mathematical formalism to construct such solutions. We work with the…
We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied : the non-propagating and the propagating one. In the first case, after proving the existence…
The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
In this paper we consider two models of soliton dynamics (the sine Gordon and the \phi^4 equations) on a 1-dimensional lattice. We are interested in particular in the behavior of their kink-like solutions inside the Peierls- Nabarro barrier…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
We give definitions for different types of moving spatially localized objects in discrete nonlinear lattices. We derive general analytical relations connecting frequency, velocity and localization length of moving discrete breathers and…
The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high energy strongly localized ``discrete'' kink-solitons (DK), which move with supersonic…
An optical kink is a shock-wave-like field structure which can appear in a resonant two-level medium as a result of the nonlinear process of self-steepening. We numerically simulate this process using an adiabatically switching waveform as…
This is the second of two companion papers dedicated to the investigation of vortex motion on non-orientable surfaces. The first paper of the pair is predominantly concerned with establishing the Hamiltonian approach to systems of point…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1+1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is…
In many Hamiltonian systems, propagation of steadily travelling solitons or kinks is prohibited because of resonances with linear excitations. We show that Hamiltonian systems with resonances may admit an infinite number of travelling…
We study the mobility of solitons in second-harmonic-generating lattices. Contrary to what is known for their cubic counterparts, discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…