Related papers: Exact solutions for discrete breathers in forced-d…
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…
Linear wave equations on flat band networks host compact localized eigenstates (CLS). Nonlinear wave equations on translationally invariant flat band networks can host compact discrete breathers - time periodic and spatially compact…
We observe dark and bright intrinsic localized modes (ILMs) or discrete breathers (DB) experimentally and numerically in a diatomic-like electrical lattice. The generation of dark ILMs by driving a dissipative lattice with…
The Discrete Nonlinear Schr\"odinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In [Iubini S, Chirondojan L, Oppo G L, Politi A and Politi P 2019…
We study anharmonic localization in a periodic five atom chain with quadratic-quartic spring potential. We use discrete symmetries to eliminate the degeneracies of the harmonic chain and easily find periodic orbits. We apply linear…
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 study the energy relaxation process in one-dimensional (1D) lattices with next-nearest-neighbor (NNN) couplings. This relaxation is produced by adding damping (absorbing conditions) to the boundary (free-end) of the lattice. Compared to…
We explore breather propagation in the damped oscillatory chain with essentially nonlinear (non-linearizable) nearest-neighbour coupling. Combination of the damping and the substantially nonlinear coupling leads to rather unusual two-stage…
We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin (discrete breathers) emerge naturally as…
In the present work, we develop a systematic examination of the existence, stability and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an…
We consider the Hamiltonian version of a $\cal PT$-symmetric lattice that describes dynamics of coupled pendula under a resonant periodic force. Using the asymptotic limit of a weak coupling between the pendula, we prove the nonlinear…
We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a)…
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…
We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the…
A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and…
We investigate the nonlinear dynamics of a damped Peyrard-Bishop DNA model taking into account long-range interactions with distance dependence |l|^-s on the elastic coupling constant between different DNA base pairs. Considering both…
This paper deals with the theoretical and numerical analysis of dynamic fracture of dissimilar chain consisting of masses lined by springs. Such a structure exhibits quite different dynamic properties in comparison with a symmetrical…
We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state…
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…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…