  We present new approaches for solving constrained multicomponent nonlinear
Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an
artificial time and solve an extended damped second order dynamic system whose
stationary solution is the solution to the time-independent nonlinear
Schr\"odinger equation. Constraints are often considered by projection onto the
constraint set, here we include them explicitly into the dynamical system. We
show the applicability and efficiency of the methods on examples of relevance
in modern physics applications.
