Article ID Journal Published Year Pages File Type
4609146 Journal of Complexity 2006 18 Pages PDF
Abstract

We study Turing computability of the solution operators of the initial-value problems for the linear Schrödinger equation ut=iΔu+φ and the nonlinear Schrödinger equation of the form iut=-Δu+mu+|u|2u. We prove that the solution operators are computable if the initial data are Sobolev functions but noncomputable in the linear case if the initial data are Lp-functions and p≠2. The computations are performed on Type-2 Turing machines.

Related Topics
Physical Sciences and Engineering Mathematics Analysis