Computing the Solutions of the Combined Korteweg-de Vries Equation by Turing Machines

In this paper, we study the computability of the initial value problem of Combined Korteweg-de Vries (CKdV, for short) equation: ut + uux + u2ux + uxxx = 0, u(x, 0) d(x). It is shown that, for any integer .v 3. the nonlinear solution operator K/< : IIs(¥i) —>• C(R,HS(R)) which maps an initial condition data (f) to the solution of the Combined KdV equation can be computed by a Turing machine.