Operator splitting for the KdV equation

We provide a new analytical approach to operator splitting for equations of the type u t = A u + B ( u ) u_t=Au+B(u) , where A A is a linear operator and B B is quadratic. A particular example is the Korteweg–de Vries (KdV) equation u t − u u x + u x x x = 0 u_t-u u_x+uₓₓₓ=0 . We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.