Partially invariant solutions of models obtained from the Nambu–Goto action
Bibliographic record
Abstract
The concept of partially invariant solutions is discussed in the framework of the group analysis of models derived from the Nambu–Goto action. In particular, we consider the nonrelativistic Chaplygin gas and the relativistic Born–Infeld theory for a scalar field. Using a general systematic approach based on subgroup classification methods, nontrivial partially invariant solutions with defect structure δ=1 are constructed. For this purpose, a classification of the subgroups of the Lie point symmetry group, which have generic orbits of dimension 2, has been performed. These subgroups allow us to introduce the corresponding symmetry variables and next to reduce the initial equations to different nonequivalent classes of partial differential equations and ordinary differential equations. The latter can be transformed to standard form and, in some cases, solved in terms of elementary and Jacobi elliptic functions. This results in a large number of new partially invariant solutions, which are determined to be either reducible or irreducible with respect to the symmetry group. Some physical interpretation of the results in the area of fluid dynamics and field theory are discussed. The solutions represent traveling and centered waves, algebraic solitons, kinks, bumps, cnoidal and snoidal waves.
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How this classification was reachedexpand
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 | 0.000 | 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".