Abstract We study admissible and equivalence point transformations between generalized multidimensional nonlinear Schrodinger equations and classify Lie symmetries of such equations. We begin with a wide superclass of Schrodinger-type equations, which includes all the other classes considered in the paper. Showing that this superclass is not normalized, we partition it into two disjoint normalized subclasses, which are not related by point transformations. Further constraining the arbitrary elements of the superclass, we construct a hierarchy of normalized classes of Schrodinger-type equations. This gives us an appropriate normalized superclass for the non-normalized class of multidimensional nonlinear Schrodinger equations with potentials and modular nonlinearities and allows us to partition the latter class into three families of normalized subclasses. After a preliminary study of Lie symmetries of nonlinear Schrodinger equations with potentials and modular nonlinearities for an arbitrary space dimension, we exhaustively solve the group classification problem for such equations in space dimension two.

中文翻译：

---

多维非线性薛定谔方程的等价群和群分类

摘要 我们研究了广义多维非线性薛定谔方程之间的容许点变换和等当点变换，并对这些方程的李对称性进行了分类。我们从薛定谔型方程的广泛超类开始，其中包括本文中考虑的所有其他类。表明这个超类没有被归一化，我们将它划分为两个不相交的归一化子类，它们与点变换无关。进一步限制超类的任意元素，我们构造了薛定谔型方程的归一化类的层次结构。这为具有势和模非线性的多维非线性薛定谔方程的非归一化类提供了适当的归一化超类，并允许我们将后一类划分为三个归一化子类。在对任意空间维度的具有势和模非线性的非线性薛定谔方程的李对称性进行了初步研究后，我们详尽地解决了此类方程在空间维度二的群分类问题。