Analytical and Numerical Investigation of Soliton Solutions of Coupled Equations in Quadratic Media: A Novel Approach
Bibliographic record
Abstract
Solitons have been hitherto studied in Kerr media. However, we show that the optical solitons are not only limited to non-linear Kerr media. In this paper, a new method is devised to achieve the analytical approximate solutions to the soliton packages in one and two dimensions. Inputting (1) and (2) to Maxwell equations and using second-harmonic generation of type I, the coupled motion equations are obtained. Some states of spatial bright solitons are studied for large values of . The variational method is briefly reviewed and analytical approximate solution to quadratic-soliton coupled motion equations is investigated in one and two dimensions and also numerically solved. The comparison of analytical and numerical results indicates that our method is more accurate than the variational method. Key words Bright and dark solitons; Spatial optical soliton; Quadratic Kerr media; Variational method; Secondharmonic generation
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".