Unitarily-invariant integrable systems and geometric curve flows in <i>SU</i> ( <i>n</i> + 1)/ <i>U</i> ( <i>n</i> ) and <i>SO</i> (2 <i>n</i> )/ <i>U</i> ( <i>n</i> )
Bibliographic record
Abstract
Abstract Bi-Hamiltonian hierarchies of soliton equations are derived from geometric non-stretching (inelastic) curve flows in the Hermitian symmetric spaces S U ( n + 1 ) / U ( n ) and S O ( 2 n ) / U ( n ) . The derivation uses Hasimoto variables defined by a moving parallel frame along the curves. As main results, new integrable multi-component versions of the Sine–Gordon (SG) equation and the modified Korteveg–de Vries (mKdV) equation, as well as a novel nonlocal multi-component version of the nonlinear Schrödinger (NLS) equation are obtained, along with their bi-Hamiltonian structures and recursion operators. These integrable systems are unitarily invariant and correspond to geometric curve flows given by a non-stretching wave map and a mKdV analog of a non-stretching Schrödinger map in the case of the SG and mKdV systems, and a generalization of the vortex filament bi-normal equation in the case of the NLS systems.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".