Equivalence groupoids and group classification of multidimensional nonlinear Schrodinger equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Kurujyibwami, Celestin¹  Popovych, Roman O.^2,3 

[1] Univ Rwanda, Coll Sci & Technol, POB 3900, Kigali, Rwanda

[2] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] NAS Ukraine, Inst Math, 3 Tereshchenkivska Str, UA-01024 Kiev, Ukraine

关键词: Nonlinear Schrodinger equations;    Equivalence groupoid;    Group classification of differential equations;    Lie symmetry;    Equivalence group;    Point transformation;   

DOI  :  10.1016/j.jmaa.2020.124271

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free