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arXiv · 2607.05796

Nowhere continuity of the flow map of an integrable derivative nonlinear Schr\"odinger system on the torus

Toshiki Kondo
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Abstract

We consider a derivative nonlinear Schr\"odinger system called the Chen-Lee-Liu type system on the torus. This system is known as a completely integrable system. We prove the flow map fails to be continuous at every point in the Sobolev space $H^s(\mathbb{T}) \times H^s(\mathbb{T})$. Moreover, we establish an additional condition required for the flow map to be continuous. For the discontinuity, we take a sequence converging to the initial data for which the corresponding solutions do not exist.

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Toshiki Kondo. 2026-07-07. Nowhere continuity of the flow map of an integrable derivative nonlinear Schr\"odinger system on the torus. https://doi.org/10.1007/s00030-026-01265-5

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