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.
翻译:我们提出了解决任意尺寸的受限制的多成分非线性Schr\'odinger方程式的新办法,目的是引入一个人为的时间,并解决一个被延长的有缺陷的第二顺序动态系统,其固定解决方案是解决时间独立的非线性非线性Schr\\'odinger方程式的解决方案。制约常常通过投射到设定的制约中来考虑,我们在这里将其明确纳入动态系统。我们用现代物理应用中的相关实例来展示这些方法的适用性和效率。