MODULATIONAL INSTABILITY OF SOLITARY WAVES IN NONDEGENERATE 3-WAVE MIXING - THE ROLE OF PHASE SYMMETRIES

We show how the analytical approach of Zakharov and Rubenchik [Sov. Ph ys. JETP 38, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schrodinger equation can be generalized for mod els with two phase symmetries. MI of three-wave parametric spatial sol itons due to group velocity dispersion (GVD) is investigated as a typi cal example of such models. We reveal a new branch of neck instability , which dominates the usual snake type MI found for normal GVD. The re sultant nonlinear evolution is thereby qualitatively different from ca ses with only a single phase symmetry. [S0031-9007(98)07369-4].