Stability analysis of spatiotemporal cnoidal waves in cubic nonlinear media

Stabilization of one-dimensional periodic waves by saturation of the nonlinear response

We address the properties of (1+1)-dimensional periodic waves in conservative saturable cubic nonlinear media and discover that cnoidal- and snoidal-type waves are completely stable within a broad range of parameters. The existence of stability bands is in sharp contrast with the previously known properties of periodic waves in self-focusing Kerr nonlinear media. We also found that in self-defocusing media instability bands occur, again in contrast to the case of Kerr media.

Stable multicolor periodic-wave arrays

We study the existence and stability of periodic-wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is the first example in physics of completely stable periodic-wave patterns propagating in conservative uniform media supporting bright solitons.

Instabilities in the two-dimensional cubic nonlinear Schrödinger equation

The two-dimensional cubic nonlinear Schrödinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with linear phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients of the linear dispersion terms have the same sign (elliptic case), then the only unstable perturbations have transverse wavelength longer than a well-defined cutoff. If the coefficients of the linear dispersion terms have opposite signs (hyperbolic case), then there is no such cutoff and as the wavelength decreases, the maximum growth rate approaches a well-defined limit.

Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media

We report theoretically the existence, classification, and basic properties of families of stationary two-dimensional cnoidal-type waves in bulk Kerr-type saturable nonlinear media. The families of two-dimensional cnoidal-type wave solutions are shown to exhibit richer features than their known one-dimensional counterparts. At low- and high-energy flows, the cnoidal patterns are predicted to be robust enough to be observable experimentally.