Lax pairs of time-dependent Gross-Pitaevskii equation

被引：36

作者：

Al Khawaja, Usama ^{[1
]}

机构：

[1] United Arab Emirates Univ, Dept Phys, Al Ain, U Arab Emirates

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2006年 / 39卷 / 31期

关键词：

D O I：

10.1088/0305-4470/39/31/002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We calculate the Lax pairs of homogeneous and inhomogeneous one-dimensional time-dependent Gross -Pitaevskii equations with time-dependent scattering length. The inhomogeneity corresponds to linear and quadratic potentials. Our approach introduces a systematic method of searching for the Lax pair corresponding to a given differential equation. We derive known Lax pairs for the Gross-Pitaevskii equation with homogeneous and quadratic potentials and time-dependent scattering length. We also derive new Lax pairs corresponding to a Gross-Pitaevskii equation with a linear potential. Using the resulting Lax pairs, the Darboux transformation can be performed and exact solutions of the Gross-Pitaevskii equation can be obtained for experimentally relevant cases such as solitonic solutions.

引用

页码：9679 / 9691

页数：13

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