New Soliton Solutions to the Space-Time Fractional Boussinesq Equation Using a Reliable Method
Bibliographic record
Abstract
Fractional partial Differential Equations (FPDEs) play an essential role in interpreting a broad variety of events in various scientific disciplines, including physics, engineering, biology, and economics. One remarkable feature of PDEs is the presence and investigation of traveling wave solutions, which are solutions that propagate with a constant speed and preserve their shape. The main purpose of this work is to obtain the traveling wave solutions of the space-time fractional Boussinesq equation using a relatively new mechanism which is the improved modified extended tanh-function approach. Fractional derivatives based on Jumarie’s modified Riemann–Liouville are utilized to deal with the fractional derivatives which appear in the fractional Boussinesq problem. Some periodic and solitary wave solutions are presented in the form of trigonometric, hyperbolic, complex, and rational functions. In addition, the effectiveness of the employed methodology is compared with the performances of other techniques such as the fractional sub-equation approach, (G’/G2)-expansion process, and the modified Kudryashov method.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.002 | 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".