Nonfocusing instabilities in coupled, integrable nonlinear Schrodinger pdes

The nonlinear coupling of two scalar nonlinear Schrodinger (NLS) fields res ults in nonfocusing instabilities that exist independently of the well-know n modulational instability of the focusing NLS equation. The focusing versu s defocusing behavior of scalar NLS fields is a well-known model for the co rresponding behavior of pulse transmission in optical fibers in the anomalo us (focusing) versus normal (defocusing) dispersion regime [19], [20]. For fibers with birefringence (induced by an asymmetry in the cross section), t he scalar NLS fields for two orthogonal polarization modes couple nonlinear ly [26]. Experiments by Rothenberg [32], [33] have demonstrated a new type of modulational instability in a birefringent normal dispersion fiber, and he proposes this cross-phase coupling instability as a mechanism for the ge neration of ultrafast, terahertz optical oscillations. In this paper the no nfocusing plane wave instability in an integrable coupled nonlinear Schrodi nger (CNLS) partial differential equation system is contrasted with the foc using instability from two perspectives: traditional linearized stability a nalysis and integrable methods based on periodic inverse spectral theory. T he latter approach is a crucial first step toward a nonlinear, nonlocal und erstanding of this new optical instability analogous to that developed for the focusing modulational instability of the sine-Gordon equations by Ercol ani, Forest, and McLaughlin [13], [14], [15], [17] and the scalar NLS equat ion by Tracy, Chen, and Lee [36], [37], Forest and Lee [:18], and McLaughli n, Li, and Overman [23], [24].