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Low-Regularity Integrator for the Davey–Stewartson II System

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Abstract

We consider the Davey–Stewartson system in the hyperbolic–elliptic case (DS-II) in two dimensional case. It is a mass-critical equation, and was proved recently by Nachman et al. (Invent Math 220(2):395–451, 2020) the global well-posedness and scattering in \(L^2\). In this paper, we give the numerical study on this model and construct a first order low-regularity integrator for the DS-II in the periodic case. It only requires the boundedness of one additional derivative of the solution to get the first order convergence. The Fast Fourier Transform is exploited to speed up the numerical implementation. By rigorous error analysis, we prove that the numerical scheme provides first order convergence in \(H^{\gamma }({\mathbb {T}}^{2})\) for rough initial data in \(H^{\gamma +1}({\mathbb {T}}^{2})\) with \(\gamma > 1\). The optimality of the convergence is conformed by numerical experience.

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All data included in this study are available upon request by contact with the corresponding author.

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Funding

C. Ning is partially supported by NSFC 11901120 and Science and Technology Program of Guangzhou, China: 2024A04J4027. X. Kou is partially supported by NSFC 12171356.

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Authors and Affiliations

  1. School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou, 510521, Guangdong, China

    Cui Ning

  2. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Xiaomin Kou & Yaohong Wang

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  1. Cui Ning
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  2. Xiaomin Kou
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  3. Yaohong Wang
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Correspondence to Yaohong Wang.

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C. Ning is partially supported by NSFC 11901120. X. Kou is partially supported by NSFC 12171356.

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Ning, C., Kou, X. & Wang, Y. Low-Regularity Integrator for the Davey–Stewartson II System. J Sci Comput 99, 10 (2024). https://doi.org/10.1007/s10915-024-02467-8

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