In this paper, we study a general nonlinear Schrödinger (NLS) equation in $\left(2,+,1\right)$ dimensions which under appropriate nonlocal symmetry reduction leads to reverse space nonlocal NLS equation. We apply Darboux transformation and construct multiple solutions of NLS equation in $\left(2,+,1\right)$ dimensions which are expressed in terms of quasideterminants. Under suitable reductions the quasideterminant formula empowers us to compute explicit expressions of symmetry broken and symmetry unbroken solutions of a generic NLS equation and $\mathcal{PT}$-symmetric reverse space nonlocal NLS equation in $\left(2,+,1\right)$ dimensions respectively. Furthermore the dynamics of symmetry broken and symmetry unbroken first two nontrivial solutions are presented. Under the dimensional reduction we obtain first- and second-order nontrivial solutions of $1+1$-dimensional nonlocal NLS equation. By applying local symmetry reduction, we obtain one- and two-soliton solutions of $2+1$-dimensional local NLS equation.

在本文中，我们研究了一般的非线性Schrödinger（NLS）方程 $\left(2,+,\mathrm{1个}\right)$在适当的非局部对称性减小下的维数导致了反向空间非局部NLS方程。我们应用Darboux变换并构造NLS方程的多个解$\left(2,+,\mathrm{1个}\right)$用四边形决定子表示的尺寸。在适当的归约条件下，quasidetermantant公式使我们能够计算泛型NLS方程的对称分解和对称不分解的显式表达式，并且$\mathcal{PT}$中的非对称逆空间非局部NLS方程 $\left(2,+,\mathrm{1个}\right)$尺寸。此外，还介绍了对称破坏和对称不破坏的动力学的前两个非平凡解。在降维的情况下，我们获得的一阶和二阶非平凡解$\mathrm{1个}+\mathrm{1个}$维非局部NLS方程。通过应用局部对称约简，我们得到了一孤子解和二孤子解$2+\mathrm{1个}$维局部NLS方程。