Novel Solutions to Fractional Nonlinear Equations for Crystal Dislocation and Ocean Shelf Internal Waves via the Generalized Bernoulli Equation Method
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The nonlinear space and time fractional (2+1)-dimensional cubic Klein-Gordon (cKG) equation and the nonlinear space and time fractional (2+1)-dimensional Gardner-KP (GKP) equation are applied to model crystal dislocation and internal waves on ocean shelves, respectively.To solve these equations, the fractional cKG and GKP equations are first converted into nonlinear ordinary differential equations (ODEs) using wave transformation and Jumarie's Riemann-Liouville derivative.The solution is then expressed as a finite series, and this approach is combined with the generalized Bernoulli equation method.Exact traveling wave solutions are obtained in the form of exponential functions, hyperbolic functions, and rational functions, which ultimately give rise to physical waves.These waves manifest in various forms, such as kink, periodic, and solitary waves, and are represented by two-dimensional and threedimensional graphical illustrations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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 it