Perturbation theory for dark–bright solitons of the Manakov system
Bibliographic record
Abstract
We present a direct perturbation method to study the dynamics of dark–bright (DB) solitons of the Manakov system under the influence of perturbations. Our methodology combines a multi-scale expansion method, perturbed conservation laws and a boundary-layer approach, which breaks the problem into an inner region, pertinent to the soliton core and an outer region, which evolves independently of the dark–bright soliton. We find that a shelf emerges around the dark soliton component, which propagates with a speed depending on the background intensity. Conserved quantities of the Manakov system are employed to determine the properties of the perturbed solutions. We focus on dissipative perturbations, such as diffusion, as well as linear and nonlinear loss, and show that the effect of the bright (filling) soliton component is to partially stabilize ‘bare’ dark solitons of the scalar case against perturbation-induced dissipation. Our analytical predictions are corroborated by results of direct numerical simulations.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".