Equivalence groupoid for (1+2)-dimensional linear Schr?dinger equations with complex potentials

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Kurujyibwami, Célestin^1,2

College of Science and Technology, University of Rwanda, P.O.Box: 3900, Kigali, Rwanda^1

Linköping University, Linköping

58183, Sweden^2

关键词: Complex potentials;    Dinger equation;    Equivalence transformations;    Groupoid;    Linear superpositions;    Point transformations;    Two equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012008/pdf
DOI  :  10.1088/1742-6596/621/1/012008

来源: IOP

【 摘 要 】

We describe admissible point transformations in the class of (1+2)-dimensional linear Schrödinger equations with complex potentials. We prove that any point transformation connecting two equations from this class is the composition of a linear superposition transformation of the corresponding initial equation and an equivalence transformation of the class. This shows that the class under study is semi-normalized.