Related papers: Breathers in PT-symmetric optical couplers
In the limit of small couplings in the nearest neighbor interaction, and small total energy, we apply the resonant normal form result of a previous paper of ours to a finite but arbitrarily large mixed Fermi-Pasta-Ulam Klein-Gordon chain,…
We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a…
We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time (PT)-symmetric system of linearly-coupled nonlinear…
We consider the evolution of the 2-soliton (breather) of the nonlinear Schroedinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard…
We study the thermodynamics of discrete breathers by transforming a lattice of weakly coupled nonlinear oscillators into an effective Ising pseudospin model. We introduce a replica ensemble and investigate the effective system…
We consider the existence and stability of solitons in a $\chi^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a…
We obtain the elementary modes of a system of parity-time reversal ( PT ) - symmetric coupled oscillators with balanced loss and gain . These modes are used to give a physical picture of the phase transition recently reported in experiments…
Strong numerical evidence is presented for the existence of a continuous family of time-periodic solutions with ``weak'' spatial localization of the spherically symmetric non-linear Klein-Gordon equation in 3+1 dimensions. These solutions…
The observation of traveling breathers (TBs) with large-amplitude oscillatory tails realizes an almost 50-year-old theoretical prediction (Kuznetsov 1975) and generalizes the notion of a breather. Two strongly nonlinear TB families are…
We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide…
We study collision processes of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on…
We consider a parity-time ($\mathcal{PT}$-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Schr\"odiner operator with localized complex…
We prove existence of real-valued, time-periodic and spatially localized solutions (breathers) of semilinear wave equations $V(x)u_{tt} - u_{xx} = \Gamma(x) |u|^{p-1} u$ on $\mathbb{R}^2$ for all values of $p\in (1,\infty)$. Using tools…
We present analytical and numerical study of discrete breathers identified as localized deformations of valence angles accompanied by change of valence bonds in crystalline polyethylene (PE). It is shown that such breathers can exist inside…
We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with…
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 consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is…
An enhancement of localized nonlinear modes in coupled systems gives rise to a novel type of escape process. We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of $N$ mass-points situated in a…
The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier…
We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a…