Computing the Solution of the m-Korteweg-de Vries Equation on Turing Machines

In this paper, we study the initial value problem of the mKdV equation, and convert the constant coefficients mKdV equation into its standard norm by linear transformation. Then, we define a nonlinear map KR:Hs(R)→C(R,Hs(R)) , from the initial data to the solution of the equation, and prove KR is Turing computable for any integer s⩾3. Therefore, the solution of the mKdV equation with arbitrary precision on Turing machines can be satisfied.