Finite and infinite soliton and kink-soliton trains of nonlinear\n Schr\\"odinger equations
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Bibliographic record
Abstract
We will first review known results on multi-solitons of dispersive partial\ndifferential equations, which are special solutions behaving like the sum of\nmany weakly-interacting solitary waves. We will then describe our recent joint\nwork with Dong Li on nonlinear Schr\\"odinger equations: Assuming the composing\nsolitons have sufficiently large relative speeds, we prove the existence and\nuniqueness of a soliton train which is a multi-soliton composed of infinitely\nmany solitons. In the 1D case, we can add to the infinite train an additional\nhalf-kink, which is a solution with a non-zero background at minus infinity.\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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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