On a three-dimensional Riccati differential equation and its symmetries

被引：1

作者：

Papillon, Charles ^{[1
]}

Tremblay, Sebastien ^{[1
]}

机构：

[1] Univ Quebec Trois Rivieres, Dept Math & Informat, Trois Rivieres, PQ G9A 5H7, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 458卷 / 01期

关键词：

Spatial Riccati equation; Complex quaternions (biquaternions); Lie point symmetries; Schrodinger operator;

D O I：

10.1016/j.jmaa.2017.09.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A three-dimensional Riccati differential equation of complex quaternion-valued functions is studied. Many properties similar to those of the ordinary differential Riccati equation such that linearization and Picard theorem are obtained. Lie point symmetries of the quaternionic Riccati equation are calculated as well as the form of the associated three-dimensional potential of the Schrodinger equation. Using symmetry reductions and relations between the three-dimensional Riccati and the Schrodinger equation, examples are given to obtain solutions of both equations. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：611 / 627

页数：17

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