Fast solitary waves against slow inertial instability in stimulated Raman scattering

Abstract

We investigate the dynamics of the backward stimulated Raman process in optical fibers; the spatiotemporal (1+1)-dimensional three-wave dissipative inertial model accounts for the noninstantaneous Raman response of the medium, the optical Kerr effect, and the group velocity dispersion. A different class of dissipative superluminous solitary structures emerges from a chaotic Stokes dynamics. In contrast with the nonlinear Schr\"odinger class of equations, the velocity of the solitary wave plays a key role and has been determined by the Kolmogorov-Petrovskii-Piskunov procedure. The long-term evolution of the three-wave resonant interaction is ruled by two competing instabilities: the convective Raman instability, characterized by the velocity of the leading front, and an ``inertial instability,'' which arises through the combined actions of the Kerr effect and the noninstantaneous response of the medium. By comparing their relative growth rates we find a criterion that determines the asymptotic pattern selected by the system (solitonlike or chaotic) and give relevant experimental parameters.