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arXiv · 2604.23202

On the construction of almost periodic solutions for the derivative nonlinear Schr\"odinger equation

Yuchen WU·Xiaoping Yuan
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Abstract

In this paper, we consider a derivative nonlinear Schr\"odinger equation $$ \mathrm{i}\partial_{t}u+\partial_{xx}u-V\ast u+\mathrm{i}\vert u\vert^{2}\partial_{x}u=0 $$ on the torus $\mathbb{T}$, depending on some potential $V$. We prove that for `almost all' potentials $V$, this equation admits an almost-periodic solution.

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Yuchen WU, Xiaoping Yuan. 2026-04-25. On the construction of almost periodic solutions for the derivative nonlinear Schr\"odinger equation. https://arxiv.org/abs/2604.23202

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