Computing wave functions of nonlinear Schrödinger equations: A time-independent approach

Two-stage continuation algorithms for Bloch waves of Bose–Einstein condensates in optical lattices

“…In [12,13] we used continuation methods to study the ground state and excited-state solutions of the following NLS: An important invariant of the NLS is the mass conservation constraint, or the normalization of the wave function…”

“…Here the chemical potential μ is treated as the continuation parameter [12,13]. We stop the curve-tracking whenever the mass conservation constraint for the stationary state wave function…”

“…Here the chemical potential μ is treated as the continuation parameter [12,13]. The other two parameters c and k ∈ [−1, 1] are keep fixed for each curve-tracking.…”

“…On the other hand, Chang, Chien and Jeng [12], and Chang and Chien [13] have studied efficient continuation algorithms for nonlinear Schrödinger equations. In this paper, we present novel two-stage continuation algorithms for computing Bloch bands/surfaces of the GPE in 1D/2D.…”

Exploring ground states and excited states of spin-1 Bose–Einstein condensates by continuation methods

“…The multi-component BECs with frozen spin degrees of freedom based on the coupled nonlinear Schrödinger equations (CNSE) have been investigated analytically and numerically [8,9,13,21]. Recently, Cao et al [17] prove the existence of the ground state for the spin-1 BEC in some cases.…”