Skryabin, Dmitry V. and Firth, William J. (1998) Modulational instability of solitary waves in nondegenerate three-wave mixing: The role of phase symmetries. Physical Review Letters, 81 (16). pp. 3379-3382. ISSN 0031-9007
We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP 38, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schrödinger equation can be generalized for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.
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