Solutions of nonlinear Schrödinger equation for interfacial waves propagating between two ideal fluids
Bibliographic record
Abstract
We present solutions to the problem of waves propagating at an interface between two inviscid fluids of infinite extent and differing densities. The method of multiple scale is employed to obtain a dispersion relation and nonlinear Schrödinger (NLS) equation, which describes the behavior of the system for the fluid interface. The dispersion relation of the model NLS equation is studied. The solutions of the NLS equation are derived analytically by using the complex tanh-function method and the function transformation method into a sine-Gordon equation. Also, diagrams are drawn to illustrate the elevation of the interface, the slip velocity, and the conservation of power. We observe that the elevation of the interface is in the form of traveling quasi-solitary waves that decrease as the wave number increases. We see that the slip velocities also bring a nonlinear and periodic characters. Finally, we observe that the conservation of power is in the form of traveling waves. Also, as the wave number increases, the conservation of power is more accurate in fluctuating around zero.
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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".