The Computability of the Initial Value Problem of Camassa-Holm Equation on Turing

In this paper we study the computability of the solution operator initial value problem of Camassa-Holm equation. Define a nonlinear map K_R from the initial date φ ∈ H^s(R) to the solution u ∈ C (R, H^s (R)). By using Sobolve spaces and Type-2 theory of effectivity, we proved that for s >; 3/2, the map K_R : H^s (R) → C (R, H^s (R)) is Turing computable and thus enrich the theory of computability on nonlinear equation´s solution.