Related papers: Breathing patterns in nonlinear relaxation
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…
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry.…
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…
Breather solutions of the nonlinear Schr\"{o}dinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a…
It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…
The passive flight of a thin wing or plate is an archetypal problem in flow-structure interactions at intermediate Reynolds numbers. This seemingly simple aerodynamic system displays an impressive variety of steady and unsteady motions that…
We prove for a class of nonlinear Schr\"odinger systems (NLS) having two nonlinear bound states that the (generic) large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
The existence and properties of envelope solitary waves on a periodic, traveling wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed point computational…
We explore dynamics of discrete breathers and multi-breathers in finite one-dimensional chain. The model involves parabolic on-site potential with rigid constraints and linear nearest-neighbor coupling. The rigid non-ideal impact…
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 propose a model for a chain of particles coupled by nonlinear springs in which each mass has an internal mass and all interactions are assumed to be nonlinear. We show how to construct an asymptotic solution of this system using multiple…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation…
We study metastable behavior in a discrete nonlinear Schr\"odinger equation from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$ sites in this equation, we consider initial conditions in which almost all the energy…
Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the…
We analytically study nonlinear quasi-monochromatic plasma waves in a two-dimensional electron system set between the two metal electrodes (gates). We derive a nonlinear Schrodinger equation for a slow-varying envelope to describe the…
The quantum modes of a nonlinear Klein Gordon lattice have been computed numerically [L. Proville, Phys. Rev. B, vol. 71, 104306 (2005)]. The on-site nonlinearity has been found to lead to a phonon pairing and consequently some phonon bound…
The nonlinear Schr\"odinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…