Stability of smooth solitary waves under intensity-dependent dispersion
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Bibliographic record
Abstract
Abstract The nonlinear Schrödinger (NLS) equation in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles that extend from the limit where the dependence of the dispersion coefficient on the wave intensity is negligible to the limit where the solitary wave becomes singular due to vanishing dispersion coefficient. We analyse and numerically explore the stability for such smooth solitary waves, showing with the help of numerical approximations that the family of solitary waves becomes unstable in an intermediate region between the two limits, while being stable in both limits. This bistability, which has also been observed in other NLS equations with generalized nonlinearity, brings about interesting dynamical transitions from one stable branch to another stable branch, which are explored in direct numerical simulations of the NLS equation with the intensity-dependent dispersion term.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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