Generation of large-amplitude solitons in the extended Korteweg–de Vries equation
Bibliographic record
Abstract
We study the extended Korteweg-de Vries equation, that is, the usual Korteweg-de Vries equation but with the inclusion of an extra cubic nonlinear term, for the case when the coefficient of the cubic nonlinear term has an opposite polarity to that of the coefficient of the linear dispersive term. As this equation is integrable, the number and type of solitons formed can be determined from an appropriate spectral problem. For initial disturbances of small amplitude, the number and type of solitons generated is similar to the well-known situation for the Korteweg-de Vries equation. However, our interest here is in initial disturbances of larger amplitude, for which there is the possibility of the generation of large-amplitude "table-top" solitons as well as small-amplitude solitons similar to the solitons of the Korteweg-de Vries equation. For this case, and in contrast to some earlier results which assumed that an initial disturbance in the shape of a rectangular box would be typical, we show that the number and type of solitons formed depend crucially on the disturbance shape, and change drastically when the initial disturbance is changed from a rectangular box to a "sech"-profile. (c) 2002 American Institute of Physics.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".