Highly dispersive eighth-order embedded solitons with cubic–quartic χ(2) and χ(3) nonlinear susceptibilities under the influence of multiplicative white noise using Itô calculus
Bibliographic record
Abstract
This research explores the intriguing realm of eighth-order embedded solitons in highly dispersive media with cubic–quartic nonlinear susceptibilities [Formula: see text] and [Formula: see text], all within the dynamic context of multiplicative white noise and the framework of Itô calculus. Two different approaches are used in this study. The new auxiliary equation approach produces the bright soliton and singular soliton solutions, while the addendum Kudryashov’s approach produces the bright soliton, singular soliton and combo bright–singular soliton solutions. The system under investigation and the results documented within this work stand as pioneering and original contributions to the field of nonlinear optics. Furthermore, a collection of 2D, 3D and contour plots is produced to visually represent the spatial distribution and progression of different solutions. This not only contributes to the advancement of nonlinear equations in theory but also offers valuable insights for practical applications.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".