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arXiv · 2504.19800

Long time asymptotics of a perturbed modified KdV equation

Gong Chen·Jiaqi Liu·Yuanhong Tian
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Abstract

We derive full asymptotics of the modified KdV equation (mKdV) with a higher-order perturbative term. We make use of the perturbative theory of infinite-dimensional integrable systems developed by P. Deift and X. Zhou \cite{DZ-2}, and some new and simpler proofs of certain $L^\infty$ bounds and $L^p$ a priori estimates developed recently in \cite{CLT}. We show that the perturbed equation exhibits the same long-time behavior as the completely integrable mKdV.

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Gong Chen, Jiaqi Liu, Yuanhong Tian. 2025-04-28. Long time asymptotics of a perturbed modified KdV equation. https://arxiv.org/abs/2504.19800

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