Search results for "Nonlinear"
showing 10 items of 3684 documents
Optical Bistability and Switching in Oppositely Directed Coupler
2016
We report the optical bistability in two core oppositely directed coupler with negative index material channel. Using Langrangian variational method and Jacobi elliptic functions, we construct the solutions of the coupled nonlinear Schrodinger equations. The bistability arises due to the effective feedback mechanism as a result of opposite directionality of the phase velocity and energy flow in the negative index material channel. We report the various ways to control and manipulate the bistability threshold and hysteresis loop, which could be useful in the design and development of fast and low-threshold optical switches.
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
2001
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…
Hydrodynamics of periodic breathers
2014
We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.
Tenth Peregrine breather solution to the NLS equation
2015
We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.
Two-dimensional mobile breather scattering in a hexagonal crystal lattice.
2021
We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an “egg-box” harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained en…
All-optical discrete vortex switch
2011
We introduce discrete vortex solitons and vortex breathers in circular arrays of nonlinear waveguides. The simplest vortex breather in a four-waveguide coupler is a nonlinear dynamic state changing its topological charge between $+1$ and $\ensuremath{-}1$ periodically during propagation. We find the stability domain for this solution and suggest an all-optical vortex switching scheme.
Collision of Akhmediev Breathers in Nonlinear Fiber Optics
2013
We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines dri…
Stochastic Response Of Fractionally Damped Beams
2014
Abstract This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system. Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional de…
COMPUTER SIMULATION OF PROFILES OF INTERFACES BETWEEN COEXISTING PHASES: DO WE UNDERSTAND THEIR FINITE SIZE EFFECTS?
2000
Interfaces between coexisting phases are very common in condensed matter physics, and thus many simulations attempt to characterize their properties, in particular, the interfacial tension and the interfacial profile. However, while theory usually deals with the "intrinsic profile", the latter is not a straightforward output of a simulation: The actual profile (observed in simulations and/or experiments!) is broadened by lateral fluctuations. Therefore, in the usual simulation geometry of L × L × L (in three dimensions), where one chooses suitable boundary conditions to stabilize one or two interfaces of (minimal) area L × L, the profile (and in particular the interfacial width) depends on…
Existence of global weak solutions to the kinetic Peterlin model
2018
Abstract We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an incompressible viscous Newtonian fluid confined to a bounded domain in two or three space dimensions. The unsteady motion of the solvent is described by the incompressible Navier–Stokes equations with the elastic extra stress tensor appearing as a forcing term in the momentum equation. The elastic stress tensor is defined by Kramer’s expression through the probability density function that satisfies the corresponding Fokker–Planck equation. In thi…