Painlevé analysis and new analytical solutions for compound KdV–Burgers equation with variable coefficients
Bibliographic record
Abstract
We consider the solutions of the compound Korteweg–de Vries (KdV)–Burgers equation with variable coefficients (vccKdV–B) that describe the propagation of undulant bores in shallow water with certain dissipative effects. The Weiss–Tabor–Carnevale (WTC)–Kruskal algorithm is applied to study the integrability of the vccKdV–B equation. We found that the vccKdV–B equation is not Painlevé integrable unless the variable coefficients satisfy certain constraints. We used the outcome of the truncated Painlevé expansion to construct the Bäcklund transformation, and three families of new analytical solutions for the vccKdV –B equation are obtained. The dispersion relation and its characteristics are illustrated. The stability for the vccKdV–B equation is analyzed by using the phase portrait method.
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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".