Creative Commons Attribution License. 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) = φ(x). It is shown that, for any integer s> 3, the nonlinear solution operator KR: Hs(R) → C(R,Hs(R)) which maps an initial condition data φ to the solution of the Combined KdV equation can be computed by a Turing machine