Lie symmetries and dynamics of invariant solutions to (3 + 1)-dimensional KP-BBM equation
Bibliographic record
Abstract
This article aims to analyze Lie symmetries and provide analytical solutions to the generalised form of the (3 + 1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation. The test equation can be employed in energy harvesting systems, transportation, the oil and gas industry, and maritime engineering. The similarity transformations method via Lie group theory is utilized to derive infinitesimal generators, and hence similarity form is obtained, which turns the test equation into an equivalent ordinary differential equation. Under appropriate parametric constraints, the ordinary differential equation provides a variety of exact solutions. We trace the profiles of the solutions to emphasize their physical significance, demonstrating their dark lump, doubly soliton, stationary, bright soliton, and line multisoliton natures. Moreover, we determine the novelty and generality of the derived solutions by comparing them to the previous outcomes. The results of this study could be useful in different fields, such as ionic-acoustic solitons, coastal engineering for modeling and assessing long surface gravity waves, and in the computer simulation of nonlinear systems.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".