Embedded exponential-type low-regularity integrators for KdV equation under rough data

In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal convergence results under rough initial data. The schemes are explicit efficient to implement. By rigorous error analysis, first show that ELRI scheme provides order accuracy in $$H^\gamma $$ data $$H^{\gamma +1}$$ $$\gamma >\frac{1}{2}$$ . Moreover, by adding two more correction terms scheme, second +3}$$ \ge 0$$ proposed ELRIs further reduce regularity requirement existing methods so far convergence. theoretical confirmed numerical experiments, comparisons with illustrate efficiency new methods.