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arXiv · 2404.16817

Modified scattering for the cubic Schr\"odinger equation on Diophantine waveguides

Nicolas Camps·Gigliola Staffilani
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Abstract

We consider the cubic Schr\"odinger equation posed on a product space subject to a generic Diophantine condition. Our analysis shows that the small-amplitude solutions undergo modified scattering to an effective dynamics governed by interactions that induce no growth of high-order Sobolev norms. This is in sharp contrast with the infinite energy cascade scenario observed by Hani--Pausader--Tzvetkov--Visciglia in the absence of Diophantine conditions.

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Nicolas Camps, Gigliola Staffilani. 2024-04-25. Modified scattering for the cubic Schr\"odinger equation on Diophantine waveguides. https://doi.org/10.1007/s40818-026-00234-6

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