Compensation Process and Generation of Chirped Femtosecond Solitons and Double-kink Solitons in Bose-Einstein Condensates with Time-dependent Atomic Scattering Length in a Time-varying Complex Potential
Bibliographic record
Abstract
Abstract We consider the one-dimensional (1D) cubic-quintic Gross--Pitaevskii (GP)nequation, which governs the dynamics of Bose--Einstein condensate (BEC) matter waves with time-varying scattering length and loss/gain of atoms in a harmonic trapping potential. We derive the integrability conditions and the compensation condition for the 1D GP equation and obtain, with the help of a cubic-quintic nonlinear Schr\"{o}dinger (NLS) equation with self-steepening and self-frequency shift, exact analytical solitonlike solutions with the corresponding frequency chirp which describe the dynamics of femtosecond solitons and double-kink solitons propagating on a vanishing background. Our investigation shows that under the compensation condition, the matter wave solitons maintain a constant amplitude, the amplitude of the frequency chirp depends on the scattering length, while the motion of both the matter wave solitons and the corresponding chirp depend on the external trapping potential. More interesting, the frequency chirps are localized and their feature depends on the sign of the self-steepening parameter. Our study also shows that our exact solutions can be used to describe the compression of matter wave solitons when the absolute value of the s-wave scattering length increases with time.
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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 | 0.000 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".