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

In this paper we are interested in gradient flow type methods for computing the ground state of nonlinear Schrodinger/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.

Automated summary

This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.