Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

Details Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

1999-06-05

arxiv.org/abs/patt-sol/9906005v1

Phys. Rev. Lett., v. 81, pp. 3379-3382 (1998)

Nonlinear Sciences

Pattern Formation and Solitons

4 pages with figures

Scientific paper

10.1103/PhysRevLett.81.3379

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schr\"oedinger equation (NLS) can be generalised 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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