MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS

Abstract

The modified Gross-Pitaevskii equation is studied in a systematical way, both theoretically and numerically. Problems such as the dimension reduction, existence and uniqueness of the ground state, generalized or new computation schemes for computing ground states and dynamics are included in the thesis. Besides, I also studied the fundamental gap problem for the Gross-Pitaevskii equation and the ground state approximations of the nonlinear Schrödinger equation, which consists a minor part of my thesis.