Symbiotic solitary-wave pairs sustained by cross-phase modulation in optical fibers

Abstract

A new class of solitary-wave envelope solutions is found to the problem of nonlinear (Kerr) interaction between two optical waves copropagating at different frequencies in an optical fiber. The solutions, consisting of pairs of (i) generalized bright and gray solitary waves and (ii) periodic solitary waves, are symbiotic in the sense that each wave in the pair depends crucially on the cross-phase modulation from the complementary wave. The solutions of type (i) admit bright pulse propagation in the normal-dispersion regime and dark (gray) pulse propagation in the anomalous-dispersion regime. A perturbation analysis indicates that the solutions of type (i) form boundary oscillatory states in the presence of small mismatches in group velocity and/or initial position.