A normal form for nonlinear resonance of embedded solitons
Bibliographic record
Abstract
A normal form for nonlinear resonance of embedded solitons is derived for a coupled two–wave system that generalizes the second–harmonic–generating model. This wave system is non–Hamiltonian in general. An embedded soliton is a localized mode of the nonlinear system that coexists with the linear wave spectrum. It occurs as a result of a codimension–one bifurcation of non–local wave solutions. Nonlinearity couples the embedded soliton and the linear wave spectrum and induces a one–sided radiation–driven decay of embedded solitons. The normal form shows that the embedded soliton is semi–stable, i.e. it survives under perturbations of one sign, but is destroyed by perturbations of the opposite sign. When a perturbed embedded soliton sheds continuous wave radiation, the radiation amplitude is generally not minimal, even if the wave system is Hamiltonian. The results of the analytical theory are confirmed by numerical computations.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".