Related papers: Some breathers and multi-breathers for FPU-type ch…
We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for…
Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying…
In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some…
We present a simple numerical method for the discrete breather construction based on the idea of the pair synchronization of the particles involved in the breather vibration. It can be used for obtaining exact breather solutions in…
For the Fermi-Pasta-Ulam chain, an effective Hamiltonian is constructed, describing the motion of approximate, weakly localized discrete breathers traveling along the chain. The velocity of these moving and localized vibrations can be…
By numerical simulation methods the interactions of oscillating solutions (breathers) of the (2+1)-dimensional O(3) nonlinear sigma model is investigated. The models of head-on collisions in which the interacting breathers, in particular,…
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation \begin{align} \partial_t^2 U - \Delta U + m^2 U = \Gamma (x) U^3 \quad \text{on } \mathbb{R} \times \mathbb{R}^3, \end{align} which are…
We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical $\phi^4$ model. The power carried by the PT-breather oscillates…
The existence, stability and movability of breathers in a model for alpha-helix proteins is studied. This model basically consists a chain of dipole moments parallel to it. The existence of localized linear modes brings about that the…
A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is…
A systematic correlation between the initial profile of discrete breathers and their frequency is described. The context is that of a very weakly harmonically coupled chain of softly anharmonic oscillators. The results are structurally…
We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical…
We consider the full set of Maxwell equations in a slab or cylindrical waveguide with a cubically nonlinear material law for the polarization of the electric field. The nonlinear polarization may be instantaneous or retarded, and we assume…
We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale…
We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalizing recent results of Herrmann and Rademacher we allow for…
In the present work, we study the nonlinear dynamics of a microtubule, an important part of the cytoskeleton. We use a two-component model of the relevant system. A crucial nonlinear differential equation is solved with semi-discrete…
Collision process between breather and moving kink-soliton is investigated both analytically and numerically in Fermi-Pasta-Ulam (FPU) chains. As it is shown by both analytical and numerical consideration low amplitude breathers and soft…
Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems…
The paper addresses compact oscillatory states (compact breathers) in translationally-invariant lattices with flat dispersion bands. The compact breathers appear in such systems even in the linear approximation. If the interactions are…
Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and…