An nth-order Darboux transformation for the one-dimensional time-dependent Schrodinger equation

被引：18

作者：

Arrigo, DJ ^{[1
]}

Hickling, F ^{[1
]}

机构：

[1] Univ Cent Arkansas, Dept Math, Conway, AR 72035 USA

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2003年 / 36卷 / 06期

关键词：

D O I：

10.1088/0305-4470/36/6/307

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Solutions for two one-dimensional Schrodinger equations are linked together using an nth-order Darboux transformation. The resulting coefficients for these Darboux transformations give rise to a system of n nonlinear partial differential equations. This system is shown to be equivalent to a matrix Burgers equation which is linearized using a generalized Hopf-Cole transformation. Solving this linear system provides the link between solutions of the two Schrodinger equations and shows how to factor an nth-order Darboux transformation into n first-order Darboux transformations.

引用

页码：1615 / 1621

页数：7

共 16 条

[11]

Matveev V. B., 1991, Darboux transformation and solitons, DOI DOI 10.1007/978-3-662-00922-2

[12] DARBOUX TRANSFORMATION AND THE EXPLICIT SOLUTIONS OF DIFFERENTIAL-DIFFERENCE AND DIFFERENCE-DIFFERENCE EVOLUTION EQUATIONS .1. [J].