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

Dmitry V. Skryabin, William J. Firth

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages3379-3382
Number of pages5
JournalPhysical Review Letters
Volume81
Issue number16
DOIs
Publication statusPublished - 19 Oct 1998

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solitary waves
symmetry
group velocity
snakes
nonlinear equations

Keywords

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

Cite this

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abstract = "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 Schr{\"o}dinger 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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Modulational instability of solitary waves in nondegenerate three-wave mixing : the role of phase symmetries. / Skryabin, Dmitry V.; Firth, William J.

In: Physical Review Letters, Vol. 81, No. 16, 19.10.1998, p. 3379-3382.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Modulational instability of solitary waves in nondegenerate three-wave mixing

T2 - Physical Review Letters

AU - Skryabin, Dmitry V.

AU - Firth, William J.

PY - 1998/10/19

Y1 - 1998/10/19

N2 - 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.

AB - 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.

KW - modulational instability

KW - solitary waves

KW - nondegenerate three-wave mixing

KW - phase symmetries

U2 - 10.1103/PhysRevLett.81.3379

DO - 10.1103/PhysRevLett.81.3379

M3 - Article

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JO - Physical Review Letters

JF - Physical Review Letters

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