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

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

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

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schroedinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing new mechanisms of decay of antidark solitons.Comment: 8 pages, 10 figures, accepted in PR

Parametric excitation of multiple resonant radiations from localized wavepackets

Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A remarkable property of such driving is that it can induce the localized (bound) states to resonantly couple to the continuum. Therefore experiments that allow for enlightening and controlling the mechanisms underlying such coupling are of paramount importance. We implement such an experiment in a special fiber optics system characterized by a dispersion oscillating along the propagation coordinate, which mimics "time". The quasi-momentum associated with such periodic perturbation is responsible for the efficient coupling of energy from the localized wave-packets sustained by the fiber nonlinearity into free-running linear dispersive waves (continuum), at multiple resonant frequencies. Remarkably, the observed resonances can be explained by means of a unified approach, regardless of the fact that the localized state is a soliton-like pulse or a shock front

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

Competing Turing and Faraday instabilities in longitudinally modulated passive resonators

We experimentally investigate the interplay of Turing and Faraday (modulational) instabilities in a bistable passive nonlinear resonator. The Faraday branch is induced via parametric resonance owing to a periodic modulation of the resonator dispersion. We show that the bistable switching dynamics is dramatically affected by the competition between the two instability mechanisms, which dictates two completely novel scenarios. At low detunings from resonance switching occurs between the stable stationary lower branch and the Faraday-unstable upper branch, whereas at high detunings we observe the crossover between the Turing and Faraday periodic structures. The results are well explained in terms of the universal Lugiato-Lefever model