Normalized fractional gradient flow for nonlinear Schrödinger/Gross–Pitaevskii equations

Abstract

In this paper we are interested in gradient flow type methods for computing the ground state of nonlinear Schrödinger/Gross–Pitaevskii equations. Fractional Normalized Gradient Flow methods, involving fractional derivatives and generalizing the celebrated Normalized Gradient Flow method (see Bao and Du, 2004) are derived and analyzed. Several experiments are proposed to illustrate some convergence properties of the developed algorithms.