Line-solitons, line-shocks, and conservation laws of a universal KP-like\n equation in 2+1 dimensions
Bibliographic record
Abstract
A universal KP-like equation in 2+1 dimensions, which models general\nnonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small\ntransversality, is studied. Special cases include the integrable KP\n(Kadomtsev-Petviashvili) equation and it is modified version, as well as their\np-power generalizations. Two main results are obtained. First, all low-order\nconservation laws are derived, including ones that arise for special powers p.\nThe conservation laws comprise momenta, energy, and Galilean-type quantities,\nas well as topological charges. Their physical meaning and properties are\ndiscussed. Second, all line-soliton solutions are obtained in an explicit form.\nA parameterization is given using the speed and the direction angle of the\nline-soliton, and the allowed kinematic region is determined in terms of these\nparameters. Basic kinematical properties of the line-solitons are also\ndiscussed. These properties differ significantly compared to those for KP\nline-solitons and their p-power generalizations. A line-shock solution is shown\nto emerge when a special limiting case of the kinematic region is considered.\n
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".