Turing Computability of the Solution Operator of the Initial Value Problem for Fifth-order Camassa-Holm Equation

The computability of the solution operator of the Cauchy problem for the Fifth-order Camassa- Holm equation is studied in this paper. Firstly, a nonlinear map KR : H s → C (R; H s (R)) is defined from the initial value φ to the solution u. Then we used the relevant knowledge of type-2 theory of effectivity, functional analysis and Sobolev space to prove that when s > (6 √ 10 − 17) / 4, the solution operator of the Cauchy problem the Fifth-order Camassa-Holm equation is computable. The conclusion enriches the theories of computability.