Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations

Dmitry V. Skryabin, William J. Firth

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18 Citations (Scopus)

Abstract

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.
LanguageEnglish
Pages1019-1029
Number of pages11
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume60
Issue number1
DOIs
Publication statusPublished - Jul 1999

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Modulational Instability
Coupled Nonlinear Schrödinger Equations
Solitary Waves
Symmetry Breaking
nonlinear equations
Polarization
solitary waves
Solitary Solution
Phase Modulation
Group Velocity
Solitary Wave Solution
broken symmetry
Numerical Stability
Threshold Value
Ground State
numerical stability
Exceed
Branch
polarization
group velocity

Keywords

  • modulational instability
  • Schrodinger equations
  • solitary solutions
  • spatial solitary waves
  • polarization
  • bright solitary waves

Cite this

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abstract = "We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr{\"o}dinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.",
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T1 - Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations

AU - Skryabin, Dmitry V.

AU - Firth, William J.

PY - 1999/7

Y1 - 1999/7

N2 - We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.

AB - We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.

KW - modulational instability

KW - Schrodinger equations

KW - solitary solutions

KW - spatial solitary waves

KW - polarization

KW - bright solitary waves

U2 - 10.1103/PhysRevE.60.1019

DO - 10.1103/PhysRevE.60.1019

M3 - Article

VL - 60

SP - 1019

EP - 1029

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

ER -