Coherent Structures in Weakly Birefringent Nonlinear Optical Fibers

Yang, Jianke

doi:10.1002/sapm1996972127

Cited by 13 publications

(4 citation statements)

References 11 publications

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“…Tan and Liu [19] and Tan [17] have derived this system for applications in geophysical fluid dynamics. The coupled-NLS has also been extensively studied in nonlinear optics where only a partial list of references includes [12,28,20,13,21,15,11,1,10,27,23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Composite bound states of wide and narrow envelope solitons in the coupled Schrödinger equations through matched asymptotic expansions

Boyd

Tan

1999

Nonlinearity

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Coupled Nonlinear Schrödinger equations, linked by cross modulation terms, arise in both nonlinear optics and in Rossby waves in the atmosphere and ocean. Numerically, Akhmediev and Ankiewicz and Haelterman and Sheppard discovered a class of soiltary waves which are composed of a tall, narrow sech-shaped soliton in one mode, bound to a pair of short, wide sech-shaped peaks in the other mode or polarization. Through the method of matched asymptotic expansions, we derive analytical approximations to these solitary waves, and to their periodic generalization, which have been hitherto accessible only through numerical computation.

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Section: Introductionmentioning

confidence: 99%

Composite bound states of wide and narrow envelope solitons in the coupled Schrödinger equations through matched asymptotic expansions

Boyd

Tan

1999

Nonlinearity

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“…(32), v grows to finite amplitude and gradually changes its shape. Yang [19] has computed the first order corrections to these Legendre modes, but numerical methods are needed to accurately trace the full solution branch emerging from these "father-daughter" solutions. The u soliton is the "father"; the infinitesimal amplitude v, solving the Associated Legendre equation, is the "daughter".…”

Section: Father-daughter Approximationsmentioning

confidence: 99%

“…Stability analyses [18][19][20] suggest that the other species of solitary waves are easily disassociated. The equal-frequency solitary waves are merely one point on a branch of solutions, but it is when the solitary waves have equal width and frequency that they are likely to have the strongest and most varied interactions.…”

Section: Solution Branchesmentioning

confidence: 99%

Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves

Tan

Boyd²

2000

Chaos, Solitons & Fractals

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Coupled Nonlinear Schrödinger equations, linked by cross modulation terms, arise in both nonlinear optics and in Rossby waves in the atmosphere and ocean. In this paper, we derive exact, analytic solutions for the "bright" coupled-mode soliton, for which the envelope in each mode asymptotes to zero at spatial infinity, and for its spatially periodic generalization. We then numerically study the collisions of the coupled-mode solitary wave both with a conventional envelope soliton, confined to a single mode, and also with a second coupled-mode solitary wave. The collisions are sensitive to both the relative speed and phase of the solitons. In some parameter ranges, the collisions are nearly elastic, but in others, one or both solitons fission.

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“…When n = 1, (1) is referred to as the cubic nonlinear Schrödinger (NLS) equation. It has been used extensively to model, among many other applications, waves in deep water [1,37,54], propagation in nonlinear optics [28,34,53], Bose-Einstein condensates [2,25,26,36,43,49], and electron plasma waves [12]. The interaction matrix α = (α jk ) n j,k=1 contains information about the nature of the interactions between the different components of the wave functions.…”

Section: Introductionmentioning

confidence: 99%

On the spectral stability of solitary wave solutions of the vector nonlinear Schrödinger equation

Deconinck

Sheils

Nguyen

et al. 2013

J. Phys. A: Math. Theor.

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Abstract. We consider a system of coupled cubic nonlinear Schrödinger (NLS) equationswhere the interaction coefficients α jk are real. The spectral stability of solitary wave solutions (both bright and dark) is examined both analytically and numerically. Our results build on preceding work by Nguyen et al. and others. Specifically, we present closed-form solitary wave solutions with trivial and non-trivial phase profiles. Their spectral stability is examined analytically by determining the locus of their essential spectrum. Their full stability spectrum is computed numerically using a large-period limit of Hill's method. We find that all nontrivial-phase solutions are unstable while some trivial-phase solutions are spectrally stable. To our knowledge, this paper presents the first investigation of the stability of the solitary waves of the coupled cubic NLS equation without the restriction that all components ψ j are proportional to sech.

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Coherent Structures in Weakly Birefringent Nonlinear Optical Fibers

Cited by 13 publications

References 11 publications

Composite bound states of wide and narrow envelope solitons in the coupled Schrödinger equations through matched asymptotic expansions

Composite bound states of wide and narrow envelope solitons in the coupled Schrödinger equations through matched asymptotic expansions

Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves

On the spectral stability of solitary wave solutions of the vector nonlinear Schrödinger equation

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