Our aim is to analyze operator splitting for the fractional Korteweg-de Vries (KdV) equation, , , where is a non-local operator with . Under the appropriate regularity of the initial data, we demonstrate the convergence of approximate solutions obtained by the Godunov and Strang splitting. Obtaining the Lie commutator bound, we show that for the Godunov splitting, first order convergence in is obtained for the initial data in and in case of the Strang splitting, second order convergence in is obtained by estimating the Lie double commutator for initial data in . The obtained rates are expected in comparison with the KdV case.

中文翻译：

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分数 Korteweg-de Vries 方程的算子分裂

我们的目标是分析分数 Korteweg-de Vries (KdV) 方程的算子分裂，, ，其中是具有 的非局部算子。在初始数据的适当规律下，我们证明了由 Godunov 和 Strang 分裂获得的近似解的收敛性。获得Lie 换向器界，我们表明对于 Godunov 分裂，获得初始数据 in 的一阶收敛，在 Strang 分裂的情况下，通过估计初始数据 in的李双换向器获得二阶收敛。与 KdV情况相比，预期获得的比率。