Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions

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 extended damped second order dynamic system whose stationary solution the time-independent equation. Constraints are often considered by projection onto constraint set, here we include them explicitly into dynamical system. show applicability efficiency of methods on examples relevance modern physics applications.