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In this paper, we introduce a first-order low-regularity integrator for the Davey–Stewartson system in the elliptic-elliptic case. It only requires the boundedness of one additional derivative of the solution to be first-order convergent. By rigorous error analysis, we show that the scheme provides first-order accuracy inHγ⁢(Td)H^{\gamma}(\mathbb{T}^{d})for rough initial data inHγ+1⁢(Td)H^{\gamma+1}(\mathbb{T}^{d})withγ&gt;d2\gamma&gt;\frac{d}{2}.

Low-Regularity Integrator for the Davey–Stewartson System: Elliptic-Elliptic Case