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.

中文翻译：

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任意维数约束多分量非线性薛定谔方程的动力学表示

我们提出了求解任意维数约束多分量非线性 Schr\"odinger 方程的新方法。其思想是引入人工时间并求解扩展阻尼二阶动态系统，其稳态解是时间无关非线性 Schr\" 的解奥丁格方程。约束通常通过投影到约束集来考虑，这里我们将它们明确地包含在动力系统中。我们在现代物理学应用中的相关示例上展示了这些方法的适用性和效率。