Modified scattering and absence of energy cascades for cubic NLS on Diophantine waveguides
Published on:
25 April 2024
Primary Category:
Analysis of PDEs
Paper Authors:
Nicolas Camps,
Gigliola Staffilani
Bullets
Key Details
Small-amplitude solutions scatter to effective dynamics
Effective dynamics governed by quasi-resonant interactions
No Sobolev norm amplification unlike periodic case
Sharp contrast indicates sensitivity to boundaries
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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 perturbations.
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