Well-posedness of scattering data for the derivative nonlinear Schr\"odinger equation in $H^s(\mathbb{R})$

Weifang Weng; Zhenya Yan

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arXiv · 2309.09234

Well-posedness of scattering data for the derivative nonlinear Schr\"odinger equation in $H^s(\mathbb{R})$

Weifang Weng·Zhenya Yan

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Abstract

We prove the well-posedness results of scattering data for the derivative nonlinear Schr\"odinger equation in $H^{s}(\mathbb{R})(s\geq\frac12)$. We show that the reciprocal of the transmission coefficient can be written as the sum of some iterative integrals, and its logarithm can be written as the sum of some connected iterative integrals. And we provide the asymptotic properties of the first few iterative integrals of the reciprocal of the transmission coefficient. Moreover, we provide some regularity properties of the reciprocal of the transmission coefficient related to scattering data in $H^{s}(\mathbb{R})$.

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BibTeX RIS

Weifang Weng, Zhenya Yan. 2023-09-17. Well-posedness of scattering data for the derivative nonlinear Schr\"odinger equation in $H^s(\mathbb{R})$. https://arxiv.org/abs/2309.09234

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