Computable Analysis of a Boundary-Value Problem for the m-Korteweg-de Vries Equation

In this paper we study the computability of the solution operator initial-boundary problem for the m-Korteweg-de Vries equation. Define a nonlinear continuous map from the space where the auxiliary data are drawn to the space of solutions. By making use of modern methods for the study of nonlinear dispersive equation and Type-2 theory of effectivity, we prove that the solution mapH^3m-1(R⁺) × H^m (0, T) → C ([0, T]; H^3m-1 (R⁺))is Turing computable for any integer and computable real numberm ≥ 2 and computable real number T >; 0.