Lie symmetry reductions and exact solutions of (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in shallow water
Bibliographic record
Abstract
This work aims to derive symmetry reductions and exact solutions of Boiti–Leon–Manna–Pempinelli (BLMP) equation using the Lie symmetry approach. The BLMP equation is highly nonlinear integrable shallow water wave model. It describes propagation of solitary waves in shallow water. The method is based on invariance property under one parameter transformation, which ensures the reducibility of test equation and results to infinitesimals. Therefore, BLMP equation reduces independent variable and gets first symmetry reductions. A twice implementation of method transforms the BLMP equation into corresponding ordinary differential equations (ODEs). Such ODEs are determined under suitable conditions and thus, derive exact solutions. These solutions are novel and never addressed in literature. The derived solutions contain various arbitrary functions and constants, therefore significant to express rich physical structures of governing phenomena. To study physical importance of the solutions and associated phenomena, these solutions have been supplemented via numerical simulations. Thus, variety of physical structures like periodic, parabolic, multisoliton, and transition in soliton nature are analyzed systematically.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.002 | 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".