Bifurcation of gap solitons through catastrophe theory

In the theory of optical gap solitons, slowly-moving finite-amplitude Lorentzian solutions are found to mediate the transition from bright to coexistent dark-antidark solitary wave pairs when the laser frequency is detuned out of the proper edge of a dynamical photonic bandgap. Catastrophe theory is applied to give a geometrical description of this strongly asymmetrical 'morphing' process.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation

We study the wave breaking mechanism for the weakly dispersive defocusing nonlinear Schrödinger equation with a constant phase dark initial datum that contains a vacuum point at the origin. We prove by means of the exact solution to the initial value problem that, in the dispersionless limit, the vacuum point is preserved by the dynamics until breaking occurs at a finite critical time. In particular, both Riemann invariants experience a simultaneous breaking at the origin. Although the initial vacuum point is no longer preserved in the presence of a finite dispersion, the critical behavior manifests itself through an abrupt transition occurring around the breaking time

Resonant radiation shed by dispersive shock waves

We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing nonlinear Schroedinger equation, giving criteria for calculating the radiated frequency based on the estimate of the shock velocity, revealing also a diversity of possible scenarios depending on the order and magnitude of the dispersive corrections

Time-reversal focusing of an expanding soliton gas in disordered replicas

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.Comment: 7 Pages, 6 Figure

The real exchange rate process and its real effects: The cases of Mexico and the USA

Exchange rate management is a salient macroeconomic issue, especially in developing countries. In this paper, we study political economy factors that may affect the real exchange rate (RER) process and the real economic effects of the RER. We review recent literature on the effects of elections on the exchange rate, and adapt Ball’s (1992) model to show that uncertainty about the future course of policy may make more appreciated RER’s less predictable. We also review the literature on the real effect of RER appreciations and of RER uncertainty. We then construct a simultaneous GARCH-M model of the joint determination of the RER and output capable of testing our hypotheses simultaneously in a single model. We estimate the model using data first from Mexico, a developing country, and the US. In Mexico we find that elections significantly affect the evolution of the RER, that more appreciated RERs are less predictable, that RER depreciations lower output growth and that RER uncertainty lowers output growth, even when controlling for its wellstudied effect on trade. By contrast, none of these effects are found in the US data.real exchange rate volatility, economic growth, electoral cycle

A collective modulation instability of multiple four-wave mixing

We investigate the modulation instability of multiple four-wave mixing arising from a dual-frequency pump in a single-mode fiber or waveguide. By applying the Floquet theory on account of the periodic nature of four-wave mixing, we reveal a collective type of instability occurring in the anomalous dispersion regime. Our interpretation of the linear stability analysis is validated by the numerical solution of the nonlinear Schroedinger equationComment: 4 pages, 3 figure

Shocks in nonlocal media

We investigate the formation of collisionless shocks along the spatial profile of a gaussian laser beam propagating in nonlocal nonlinear media. For defocusing nonlinearity the shock survives the smoothing effect of the nonlocal response, though its dynamics is qualitatively affected by the latter, whereas for focusing nonlinearity it dominates over filamentation. The patterns observed in a thermal defocusing medium are interpreted in the framework of our theory.Comment: 5 pages, 5 figure

Modulational instability in dispersion oscillating fiber ring cavities

We show that the use of a dispersion oscillating fiber in passive cavities significantly extend modulational instability to novel high-frequency bands, which also destabilize the branches of the steady response which are stable with homogeneous dispersion. By means of Floquet theory, we obtain exact explicit expression for the sideband gain, and a simple analytical estimate for the frequencies of maximum gain. Numerical simulations show that stable stationary trains of pulses can be excited in the cavity