Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator
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Bibliographic record
Abstract
. We consider the large pump-detuning limit of the Optical Parametric Oscillator equations which scale as either a focusing or defocusing parametrically forced nonlinear Schrodinger equation. Linearizing about the pulse or front solutions leads to a non-sectoral, non-self adjoint linear eigenvalue problem which we analyze 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. Key words. Parametric nonlinear Schrodinger, renormalization group, orbital stability, spectral localization. AMS subject classifications. 34D05, 35P15, 78A60 1. Introduction. The optical parametric oscillator (OPO) has attracted considerable attention in recent years due to its potential application as a source of broadly tunable coherent radiation, patte...
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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