Keith Promislow and J Nathan Kutz 2000 Nonlinearity 13 675 doi:10.1088/0951-7715/13/3/310
Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator
Keith Promislow
and J Nathan Kutz
Recommended by A Kupiainen
We consider the large pump-detuning limit of the optical parametric oscillator equations which scale as either a focusing or defocusing parametrically forced nonlinear Schrödinger equation. Linearizing about the pulse or front solutions leads to a non-sectoral, non-self-adjoint linear eigenvalue problem which we analyse via a non-perturbative method, localizing the point spectrum to regions of the complex plane. We establish H 1 linear decay estimates for the semi-group and employ renormalization group methods to demonstrate the nonlinear asymptotic stability of the solutions to small H 1 perturbations of initial conditions.
- PACS
- MSC
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35P15 Estimation of eigenvalues, upper and lower bounds
78A60 Lasers, masers, optical bistability, nonlinear optics (See also 81V80)
- Subjects
- Dates
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Issue 3 (May 2000)
Received 2 September 1999, in final form 2 February 2000
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Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator
Keith Promislow and J Nathan Kutz 2000 Nonlinearity 13 675
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