Turing Computability of a Nonlinear Schrödinger Propagator

Abstract

We study Turing computability of the nonlinear solution operator S of the Cauchy problem for the Schrödinger equation of the form

$$ i\frac{{du}} {{dt}} = - \frac{{d^2 u}} {{dx^2 }} + mu + \left| u \right|^2 u $$

in ℝ.We prove that S is a computable operator from H¹(ℝ) to C(ℝH ¹(ℝ))with respect to the canonical representations.