Observation of the buildup of modulational instability from wave breaking

Integrability and Linear Stability of Nonlinear Waves

It is well known that the linear stability of solutions of 1 + 1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N × N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N = 3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

Competing wave-breaking mechanisms in quadratic media

We show that second-harmonic generation in the regime of weak dispersion/diffraction can exhibit a coexistence of wave breaking mechanisms, such that a gradient catastrophe yielding a dispersive shock wave competes with modulational instability, leading to the generation of wavetrains with incommensurate frequencies and eventually to the destruction of the shock wave-train.

Buildup of terahertz vector dark-soliton trains from induced modulation instability in highly birefringent optical fiber

We present the experimental observation of generation of vector dark-soliton pulse trains with terahertz repetition rates in the normal dispersion regime of an optical fiber. The polarization solitons build up from induced cross-phase modulation instability of two orthogonal pumps in a highly birefringent fiber.