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On a two-dimensional planar parity-time-($\mathcal{PT}$-)symmetric nonlinear magnetic metamaterial, consisting of split-ring dimers with balanced gain and loss, discrete breather solutions can be found. We extend these studies and by…
We consider the quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. Quantum breather states are found in the middle of the energy spectrum of the confined nonescaping states of the system. They are…
We study metastable motions in weakly damped Hamiltonian systems. These are believed to inhibit the transport of energy through Hamiltonian, or nearly Hamiltonian, systems with many degrees of freedom. We investigate this question in a very…
We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a class of Fermi-Pasta-Ulam lattices representing an uncompressed chain of beads interacting via Hertz's contact forces. We then consider the…
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…
We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups. We review…
We report on the experimental generation of discrete breather states (intrinsic localized modes) in frustrated Josephson arrays. Our experiments indicate the formation of discrete breathers during the transition from the static to the…
The aim of this work is to review and also explore even further the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In…
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…
We introduce a one dimensional parity-time (PT)-symmetric nonlinear magnetic metamaterial consisted of split ring dimers having both gain and loss. When nonlinearity is absent we find a transition between an exact to a broken PT-phase; in…
We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its non-dimensionalized Hamiltonian form and its linear spectrum is examined.…
We introduce a topology-based nonlinear network model of protein dynamics with the aim of investigating the interplay of spatial disorder and nonlinearity. We show that spontaneous localization of energy occurs generically and is a…
We study localized waves in chains of oscillators coupled by Hertzian interactions and trapped in local potentials. This problem is originally motivated by Newton's cradle, a mechanical system consisting of a chain of touching beads subject…
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…
We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we…
The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a…
Artificial intelligence in the form of deep learning is now very popular and directly implemented in many areas of science and technology. In the present work we study time evolution of Discrete Breathers in one-dimensional nonlinear chains…
We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2-D hexagonal non-linear lattice. The lattice is subject to an on-site potential in addition…
The Discrete NonLinear Schr\"odinger (DNLS) equation displays a parameter region characterized by the presence of localized excitations (breathers). While their formation is well understood and it is expected that the asymptotic…
We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by…