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arXiv · 2512.21536

Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities

Yuan Li·Qiaoyuan Cheng·Engui Fan
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Abstract

We establish the global existence of solutions to the Fokas-Lenells equation for any initial data in a weighted Sobolev space $H^{3}(\mathbb{R})\cap H^{2,1}(\mathbb{R})$.This result removes all spectral restrictions on the initial data required in our previous work. The proof primarily relies on the inverse scattering transform formulated as new Riemann-Hilbert problems and Zhou's $L^{2}$-Sobolev bijectivity theory.

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Yuan Li, Qiaoyuan Cheng, Engui Fan. 2025-12-25. Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities. https://arxiv.org/abs/2512.21536

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