Infinite soliton and kink-soliton trains for nonlinear Schr\\"odinger\n equations
Why this work is in the frame
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Bibliographic record
Abstract
We look for solutions to generic nonlinear Schr\\"odinger equations build upon\nsolitons and kinks. Solitons are localized solitary waves and kinks are their\nnon localized counter-parts. We prove the existence of infinite soliton trains,\ni.e. solutions behaving at large time as the sum of infinitely many solitons.\nWe also show that one can attach a kink at one end of the train. Our proofs\nproceed by fixed point arguments around the desired profile. We present two\napproaches leading to different results, one based on a combination of\ndispersive estimates and Strichartz estimates, the other based only on\nStrichartz estimates.\n
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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