title: Bose-Einstein condensates in the presence of a magnetic trap and optical lattice.
abstract: In this paper we consider solutions of a nonlinear Schrodinger equation with a parabolic and a periodic potential motivated from the dynamics of Bose-Einstein condensates. Our starting point is the corresponding linear problem which we analyze through regular perturbation and homogenization techniques. We then use Lyapunov-Schmidt theory to establish the persistence and bifurcation of the linear states in the presence of attractive and repulsive nonlinear inter-particle interactions. Stability of such solutions is also examined and a count is given of the potential real, complex and imaginary eigenvalues with negative Krein signature that such solutions may possess. The results are corroborated with numerical computations.
authors.affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA. kapitula@math.unm.edu
authors.forename: Todd
authors.initials: T
authors.lastname: Kapitula
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008280:Magnetics; D017711:Nonlinear Dynamics; D055095:Optics and Photonics; D011789:Quantum Theory