Dynamical representations of constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions

TL;DR

This paper introduces a novel dynamical systems approach to solve constrained multicomponent nonlinear Schrödinger equations in any dimension, explicitly incorporating constraints into the system for improved efficiency.

Contribution

The authors develop a new method that embeds constraints directly into a damped second order dynamic system for solving nonlinear Schrödinger equations.

Findings

Method effectively handles constraints in Schrödinger equations

Applicable to high-dimensional physics problems

Demonstrates efficiency on relevant examples

Abstract

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.