Search results for "Nonlinear system"
showing 10 items of 1446 documents
Breathing solitary waves in a Sine-Gordon two-dimensional lattice.
1995
We study theoretically and numerically the dynamical behavior of a two-dimensional sine-Gordon lattice. We show that, via modulational instability, an initial-low-amplitude plane wave can evolve spontaneously into moving localized modes with large amplitude. These nonlinear modes, with dimensions depending on the characteristic wavelengths of the instability, behave like breathing solitary waves and present particlelike properties.
Efficient control of the energy exchange due to the Manakov vector-soliton collision
2003
By examining the concept of energy exchange among the orthogonally polarized components of each of two colliding (Manakov-like) vector solitons it is observed that a maximum or an efficient energy-exchange process is possible only for an appropriate choice of the initial physical parameters (namely, frequency separation, polarizations, time delay, and pulse-width separation between the colliding solitons) for which L(W) (walk-off length) >>L(NL) (nonlinear length). However, in this case only, the amount of energy-exchange can be considerably increased or decreased by appropriately changing the phases of colliding solitons without altering the walk-off length and the initial energy distribut…
A Look at Some Remarkable Mathematical Techniques
1996
The nonlinear equations that we have encountered in the previous chapters can be solved by using mathematical techniques such as the powerful inverse scattering transform (IST) (Gardner et al. 1967) and the remarkable Hirota method (Hirota 1971). Specifically, in addition to the one-soliton solutions, explicit multisoliton solutions representing the interaction of any number of solitons can be constructed. Moreover, in several cases a precise prediction, closely related to experiments, can be made by the IST of the nonlinear response of the physical system, that is, of the number of solitons that can emerge from a finite initial disturbance (Zakharov, 1980. Ablowitz and Segur 1981; Calogero…
Dissipative rogue wave generation from a mode-locked fiber laser experiment
2012
Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser operating in a chaotic multiple-pulse regime. These fluctuations result from ceaseless nonlinear interactions between pulses.
Analytical Dynamics of Optical Similaritons
2007
We analytically describe the attraction of parabolic pulses towards a self-similar state in weakly dispersive nonlinear fibers with linear gain.
Supercontinuum spectral control
2009
Supercontinuum (SC) generation in photonic crystal fibers (PCFs) is a cutting-edge phenomenon extensively studied in recent years [1]. SC has found many scientific and technological applications. The control of the SC spectral characteristics is crucial in most of them. A pioneering attempt in this direction was reported in Ref. [2]. We point out that SC is typically generated by accessing the anomalous dispersion regime of the fiber, i.e., when the group velocity dispersion (GVD) coefficient is lower than zero, β 2 ≪0. The recent achievement of soft-glass PCFs, namely, PCFs made up of a transparent material that shows higher nonlinear response than the widely used fused silica, opens new p…
Parametric coherent oscillation with feedback via an orthogonally polarized wave
1999
Coherent light amplification with photorefractive crystals may be a consequence of several frequency degenerate (or nearly degenerate) processes of nonlinear wave mixing : It appears for two- beam coupling in the crystals with diffusion-driven charge transport [1] or transport via circular photovoltaic currents [2].
Stationary semiconductor equations
1996
The behaviour of a semiconductor device is usually modelled by three coupled nonlinear partial differential equations of elliptic type. Such a system for the transport of mobile charge carriers was first introduced by Van Roosbroeck [Van Roosbroeck] in 1950. Nowadays there are many models which differ in their choice of unknowns, scales, various types of nonlinearities etc. (see, e.g., [Brezzi], [Groger], [Markowich], [Markowich, Ringhofer, Schmeiser], [Mock, 1972], [Polak, den Heijer, Schilders, Markowich], [Pospisek], [Pospisek, Segeth, Silhan], [Selberherr], [Sze], [Zlamal, 1986]).
Relaxation of polar order in suspensions with Quincke effect
2014
The Quincke effect---spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field---is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension…