It looks like there's only one paper in this tag, so it's history isn't too exciting, but you can still check it out below!
April 2024
Modified scattering and absence of energy cascades for cubic NLS on Diophantine waveguides
This paper studies the cubic nonlinear Schrödinger equation on product spaces satisfying a Diophantine condition. It shows that small-amplitude solutions exhibit modified scattering to an effective dynamics that does not amplify Sobolev norms. This contrasts with the infinite energy cascade observed without Diophantine conditions, indicating sensitivity to boundary pert...
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