Operator splitting for dispersion-generalized Benjamin-Ono equations

We consider the operator splitting for a class of nonlinear equation, which includes the KdV equation, the Benjamin-Ono equation, and the Burgers equation. We prove a first-order approxomation in $\mathrm{\Delta }t$ in the Sobolev space for the Godunov splitting, and second-order approximation for the Strang splitting.