Inverse scattering transform for wave-wave scattering

Chu, Flora Y. F.; Scott, Alwyn C.

doi:10.1103/physreva.12.2060

Cited by 143 publications

(36 citation statements)

References 10 publications

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“…The Lax pair for SRS has been written in the case g(k) = δ(k − k 0 ) in [28] and regularized by means of the parameter k in [20] which found its physical meaning in [16]. Dirichlet conditions are prescribed on the line x = 0 , t > 0, 2) and on the line x > 0 , t = 0,…”

Section: Boundary Values and Lax Pairmentioning

confidence: 99%

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

León¹,

Spire²

2001

J. Phys. A: Math. Gen.

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The inverse spectral transform for the Zakharov-Shabat equation on the semi-line x > 0 is reconsidered as a Hilbert problem. The boundary data induce an essential singularity as k → ∞ to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes as O(1/k) at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.

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Section: Boundary Values and Lax Pairmentioning

confidence: 99%

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

León¹,

Spire²

2001

J. Phys. A: Math. Gen.

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“…Instead they are related to the continuous spectrum (they are not solitons) and named Raman spikes [6]. Therefore the question of the observation of the Raman soliton is open since the original work [3] in 1975.…”

Section: Introductionmentioning

confidence: 99%

“…This essentially nonlinear phenomenon couples two electromagnetic waves (pump and Stokes waves) to a two-level medium and is described by a simple system of partial differential equations [3]. Such a system applies to different physical situations, depending on a phenomenological damping factor chosen to match the observed Raman linewidth.…”

Section: Introductionmentioning

confidence: 99%

“…Here the system possesses a Lax pair [3,7,8] and can be treated by means of the inverse scattering transform (IST) generalized to boundary-value problems [9,10]. The observation of the Raman soliton is an interesting open problem, especially since the boundary-value problem for TSRS has been completely solved on the finite interval in [11] with the essential result that, as expected from the works [12,13,14], the field q(x, t) universally evolves toward the self-similar solution.…”

Section: Introductionmentioning

confidence: 99%

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Raman solitons in transient SRS

Boiti¹,

Caputo²,

León³

et al. 2000

Inverse Problems

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We report the observation of Raman solitons on numerical simulations of transient stimulated Raman scattering (TSRS) with small group velocity dispersion. The theory proceeds with the inverse scattering transform (IST) for initial-boundary value problems and it is shown that the explicit theoretical solution obtained by IST for a semi-infinite medium fits strikingly well the numerical solution for a finite medium. We understand this from the rapid decrease of the medium dynamical variable (the potential of the scattering theory). The spectral transform reflection coefficient can be computed directly from the values of the input and output fields and this allows to see the generation of the Raman solitons from the numerical solution. We confirm the presence of these nonlinear modes in the medium dynamical variable by the use of a discrete spectral analysis.

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“…1 -23 It has been known for some time that the equations describing dispersionless twowave SRS (the interaction of the pump and first Stokes fields) have a soliton solution in the extreme transient limit. 5 Initially, it was believed that an instantaneous p phase shift had to be imposed on the input Stokes field for this soliton solution to be realized experimentally. 6,7 It was then discovered that Raman solitons could arise spontaneously from vacuum phase fluctuations of the Stokes field.…”

mentioning

confidence: 99%

Ultrabroad-bandwidth multifrequency Raman soliton pulse trains

McDonald

1995

Opt. Lett.

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Inverse scattering transform for wave-wave scattering

Cited by 143 publications

References 10 publications

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

Raman solitons in transient SRS

Ultrabroad-bandwidth multifrequency Raman soliton pulse trains

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