Quasi-periodic solutions of a non-autonomous KdV-mKdV equation with periodic unbounded conditions
Bibliographic record
Abstract
In this paper, the non-chiral boundary of the mixed kdv-mkdv equation is transformed into a chiral boundary by the construction of auxiliary functions, and a new linear difference format is constructed for the chiral boundary problem.Based on the traditional difference format, explicit and implicit differences are used alternately to construct a class of explicit-implicit (E-I) and implicit-explicit (I-E) alternating difference formats, and the unconditional stability of the numerical solutions is proved by taking advantage of the symmetric discrete numerical advantage of this class of alternating difference formats.The exact solution of the kdv-mkdv equation and its dynamical behavior are explored in the calculations using the semi-fixed separation of variables method combined with the phase diagram method for planar dynamical systems.Various types of exact solutions of the equations are obtained under special parametric conditions, and the existence problem of isolated wave solutions of the kdvmkdv equations is analyzed in conjunction with the exact solutions of the equations.Numerical examples verify the accuracy and feasibility of the constructed differential format, indicating the existence of isolated wave solutions for the KdV-mKdV equation.
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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 | 0.000 | 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".