A continuation BSOR-Lanczos–Galerkin method for positive bound states of a multi-component Bose–Einstein condensate

Gauss–Seidel-type methods for energy states of a multi-component Bose–Einstein condensate

“…The TSSP is explicit, unconditionally stable, time reversible and time transverse invariant if the VGPE has good resolution in the semiclassical regime, and it has a spectral order accuracy in space and second order accuracy in time (3). Recently, a continuation BSOR Lanczos-Galerkin method (12) for computing positive bound states of a multi-component BEC is developed by solving the time-independent VGPE. Furthermore, only a few numerical simulations on a multi-component BEC (14; 18; 22) have been studied.…”

“…From both theoretical and computational points of view, our proposed iterative methods are distinct from the NGF and TSSP methods in that ours are inspired by the eigenvalue problem approach for computing the ground states and the other positive bound states of a multi-component BEC. Furthermore, our methods can be combined with the continuation BSOR Lanczos-Galerkin method (12) for solving the timeindependent VGPE efficiently. This paper is organized as follows.…”

A hyperplane-constrained continuation method for near singularity in coupled nonlinear Schrödinger equations

“…Eq. (8) implies that the matrix G x (y(s)) is actually singular with the corresponding singular vector (φ 1 , φ 2 ) . Consequently, we may have a one-dimensional solution set with tangent vector (φ 1 , φ 2 ) of (1) for a fixed β 12…”

“…For the time-independent case, a Gauss-Seideltype iteration has been proposed in [9]. Furthermore, a continuation BSOR-Lanczos-Galerkin method has been developed in [8,18]. More recently, the technique of Liapunov-Schmidt reduction and continuation method has been developed in [7].…”

A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations

“…The induced problem consequently becomes an eigenvalue problem. Numerical schemes such as [4,5,[7][8][9] have been developed for solving such eigenvalue problems. However, they are not suitable for the target problem considered here.…”