Energy minimization related to the nonlinear Schrödinger equation

Authors:
Nauman Raza;Sultan Sial;Shahid S. Siddiqi;Turab Lookman
Affiliations:
Department of Mathematics, University of the Punjab, House No. 15, Street No. 39, Lahore, Pakistan and Lahore University of Management Sciences, Lahore, Pakistan;Department of Mathematics, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt. 54792, Pakistan;Department of Mathematics, University of the Punjab, House No. 15, Street No. 39, Lahore, Pakistan;Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

In this the window of the Sobolev gradient technique to the problem of minimizing a Schrodinger functional associated with a nonlinear Schrodinger equation. We show that gradients act in a suitably chosen Sobolev space (Sobolev gradients) can be used in finite-difference and finite-element settings in a computationally efficient way to find minimum energy states of Schrodinger functionals.