Question
Lax pairs can be used to solve for the equations of motion in systems with this property. For 10 points each:
[10m] Name this property of dynamical systems that have as many constants of motion as degrees of freedom, thus preventing chaotic orbits. Systems with this property, as their name implies, tend to be solvable analytically using quadratures.
ANSWER: integrability [or integrable; accept complete integrability]
[10h] Lax pairs were introduced to solve this standard integrable PDE. This equation is the continuum limit of the Fermi–Pasta–Ulam problem and can be solved analytically using a squared hyperbolic secant function.
ANSWER: KdV equation [or Korteweg–De Vries equation]
[10e] The KdV equation is solved by applying an “inverse transform” named for this process, which is also the basis for solving the Lax equation. Classical examples of this process include ones named for Rayleigh and Compton.
ANSWER: scattering [accept inverse scattering transform; accept Rayleigh scattering or Compton scattering]
<Chicago B, Physics>
Summary
| California | 2025-02-01 | Y | 3 | 13.33 | 100% | 33% | 0% |
| Florida | 2025-02-01 | Y | 3 | 13.33 | 100% | 0% | 33% |
| Lower Mid-Atlantic | 2025-02-01 | Y | 6 | 10.00 | 83% | 17% | 0% |
| Midwest | 2025-02-01 | Y | 6 | 15.00 | 100% | 17% | 33% |
| North | 2025-02-01 | Y | 3 | 13.33 | 100% | 33% | 0% |
| Northeast | 2025-02-01 | Y | 5 | 16.00 | 100% | 40% | 20% |
| Overflow | 2025-02-01 | Y | 5 | 12.00 | 100% | 0% | 20% |
| South Central | 2025-02-01 | Y | 2 | 20.00 | 100% | 50% | 50% |
| Southeast | 2025-02-01 | Y | 4 | 12.50 | 100% | 25% | 0% |
| UK | 2025-02-01 | Y | 10 | 14.00 | 100% | 30% | 10% |
| Upper Mid-Atlantic | 2025-02-01 | Y | 8 | 11.25 | 88% | 25% | 0% |
| Upstate NY | 2025-02-01 | Y | 3 | 6.67 | 67% | 0% | 0% |
Data
| Illinois A | Chicago A | 10 | 10 | 10 | 30 |
| Chicago D | Illinois B | 0 | 0 | 10 | 10 |
| Illinois C | Chicago C | 0 | 0 | 10 | 10 |
| Indiana B | Indiana A | 0 | 0 | 10 | 10 |
| WashU B | Missouri | 0 | 10 | 10 | 20 |
| WashU A | Missoui S&T | 0 | 0 | 10 | 10 |