Modulational instability of solitary waves in nondegenerate three-wave mixing: the role of phase symmetries

Dmitry V. Skryabin, William J. Firth

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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.
Original languageEnglish
Pages (from-to)3379-3382
Number of pages5
JournalPhysical Review Letters
Issue number16
Publication statusPublished - 19 Oct 1998


  • modulational instability
  • solitary waves
  • nondegenerate three-wave mixing
  • phase symmetries

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