On the Global Behavior of Solutions of a Coupled System of Nonlinear Schrödinger Equation
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Bibliographic record
Abstract
We mainly study a system of two coupled nonlinear Schrödinger equations where one equation includes gain and the other one includes losses. This model constitutes a generalization of the model of pulse propagation in birefringent optical fibers. We aim in this study at partially answering a question of some authors in [1]: “Is the H 1 ‐norm of the solution globally bounded in the Manakov case, when ?” We found that in the Manakov case, and when , the solution stays in , and also that the H 1 ‐norm of the solution cannot blow up in finite time. In the Manakov case, an estimate of the total energy is provided, which is different from that has been given in [1]. These results are corroborated by numerical results that have been obtained with a finite element solver well adapted for that purpose.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it