Скачать или смотреть Solvability is Symmetry: Solitons and Supersymmetry | Differential Equations #4

We ask a fundamental question: why are some equations exactly solvable while others are chaotic? The answer lies in symmetry. When a differential equation admits a continuous group of transformations that map solutions to solutions (a lie group), we can use that symmetry to reduce the order of the equation or find conservation laws. In rare, "miraculous" cases, a system possesses infinite symmetry. These are completely integrable systems, where nonlinear waves (solitons) behave like fundamental particles, passing through each other without scattering.

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00:00 Intro
02:15 Lie Symmetry
09:51 Noether's Theorem
15:26 Completely Integrable Systems
18:52 Inverse Scattering / Lax Pair
24:35 SUSY Quantum Mechanics