Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core

We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.Comment: 19 pages, 4 figure

Pole dynamics for the Flierl-Petviashvili equation and zonal flow

We use a systematic method which allows us to identify a class of exact solutions of the Flierl-Petvishvili equation. The solutions are periodic and have one dimensional geometry. We examine the physical properties and find that these structures can have a significant effect on the zonal flow generation.Comment: Latex 40 pages, seven figures eps included. Effect of variation of g_3 is studied. New references adde

Discrete Breathers in Two-Dimensional Anisotropic Nonlinear Schrodinger lattices

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 localized pulses from the weakly coupled regime (strongly anisotropic) to the homogeneous one (isotropic). Mobile discrete breathers are seen to be a superposition of a localized mobile core and an extended background of two-dimensional nonlinear plane waves. This structure is in agreement with previous results on onedimensional breather mobility. The study of the stability of both pinned and mobile solutions is performed using standard Floquet analysis. Regimes of quasi-collapse are found for both types of solutions, while another kind of instability (responsible for the discrete breather fission) is found for mobile solutions. The development of such instabilities is studied, examining typical trajectories on the unstable nonlinear manifold.Comment: 13 pages, 9 figure

On classification of intrinsic localized modes for the Discrete Nonlinear Schr\"{o}dinger Equation

We consider localized modes (discrete breathers) of the discrete nonlinear Schr\"{o}dinger equation $i\frac{d\psi_n}{dt}=\psi_{n+1}+\psi_{n-1}-2\psi_n+\sigma|\psi_n|^2\psi_n$, $\sigma=\pm1$, $n\in \mathbb{Z}$. We study the diversity of the steady-state solutions of the form $\psi_n(t)=e^{i\omega t}v_n$ and the intervals of the frequency, $\omega$, of their existence. The base for the analysis is provided by the anticontinuous limit ($\omega$ negative and large enough) where all the solutions can be coded by the sequences of three symbols "-", "0" and "+". Using dynamical systems approach we show that this coding is valid for $\omega<\omega^*\approx -3.4533$ and the point $\omega^*$ is a point of accumulation of saddle-node bifurcations. Also we study other bifurcations of intrinsic localized modes which take place for $\omega>\omega^*$ and give the complete table of them for the solutions with codes consisting of less than four symbols.Comment: 33 pages, 14 figures. To appear in Physica

Stationary localized states due to nonlinear impurities described by the modified discrete nonlinear Schr\"odinger equation

The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a perfectly nonlinear chain is also considered. Phase diagrams of localized states for all systems are presented. From the mean square displacement calculation, it is found that all states are not localized even though the system comprises random nonlinear site energies. Stability of the states is discussed.Comment: Six pages including five figure

Transverse Instability of Solitons Propagating on Current-Carrying Metal Thin Films

Small amplitude, long waves travelling over the surface of a current-carrying metal thin film are studied. The equation of motion for the metal surface is determined in the limit of high applied currents, when surface electromigration is the predominant cause of adatom motion. If the surface height h is independent of the transverse coordinate y, the equation of motion reduces to the Korteweg-de Vries equation. One-dimensional solitons (i.e., those with h independent of y) are shown to be unstable against perturbations to their shape with small transverse wavevector.Comment: 25 pages with 2 figures. To appear in Physica

Self-trapping and stable localized modes in nonlinear photonic crystals

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.Comment: 4 pages (RevTex) with 5 figures (EPS

Quasi-Two-Dimensional Dynamics of Plasmas and Fluids

In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente