On the splitting method for the nonlinear Schrödinger equation with initial data in H1.

In this paper, we establish a convergence result for the operator splitting scheme Z_τ introduced by Ignat [12], with initial data in H¹, for the nonlinear Schrödinger equation: ∂_tu = iΔu + iλ|u|^Pu, u(x,0) = φ(x), where p > 0, λ ∈ {−1,1}, and (x,t) ∈ R^d × [0, ∞). We prove the L² convergence of order O(τ^1/2) for the scheme with initial data in the space H¹(R^d) for the energy-subcritical range of p. [ABSTRACT FROM AUTHOR]