On the transverse instability of the two-dimensional Benjamin–Ono solitons
Bibliographic record
Abstract
The paper presents a stability analysis of plane solitons in hydrodynamic shear flows obeying a (2+1) analogue of the Benjamin–Ono equation. The analysis is carried out for the Fourier transformed linearized (2+1) Benjamin–Ono equation. The instability region and the short-wave instability threshold for plane solitons are found numerically. The numerical value of the perturbation wave number at this threshold turns out to be constant for various angles of propagation of the solitons with respect to the main shear flow. The maximum of the growth rate decreases with the increasing angle and becomes equal to zero for the perpendicular propagation. Finally, the dependency of the growth rate on the propagation angle in the long-wave limit is determined and the existence of a critical angle which separates two types of behavior of the growth rate is demonstrated.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".