论文标题
多维非线性schrödinger方程的等效组和组分类
Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations
论文作者
论文摘要
我们研究了通用多维非线性schrödinger方程之间的可接受和等效点的变换，并对此类方程式的对称性进行了分类。我们从Schrödinger-type方程的广泛超级类别开始，其中包括本文中考虑的所有其他类别。表明该超类未归一化，我们将其分为两个不相交的亚类，这与点转换无关。进一步限制了超类的任意元素，我们构建了归一化类别schrödinger-type方程的层次结构。这为我们提供了适当的归一化超类，用于具有电势和模块化非线性的多维非线性非线性schrödinger方程，使我们能够将后者类别分为三个归一化亚类的家族。在对非线性schrödinger方程的谎言对称性进行了初步研究之后，我们对任意空间维度的势和模块化非线性进行了详尽地解决了空间维度中此类方程的组分类问题。
We study admissible and equivalence point transformations between generalized multidimensional nonlinear Schrödinger equations and classify Lie symmetries of such equations. We begin with a wide superclass of Schrödinger-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 Schrödinger-type equations. This gives us an appropriate normalized superclass for the non-normalized class of multidimensional nonlinear Schrödinger 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 Schrödinger 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.
