兰州大学机构库 >数学与统计学院
非自治GP方程组的N-Darboux变换和守恒律
Alternative TitleN-fold Darboux transformation and Conservation Law for the nonautonomous GP system
郑丹丹
Thesis Advisor赵敦
2014-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword非自治GP方程组 旋量玻色-爱因斯坦凝聚 Darboux变换 守恒律
Abstract玻色-爱因斯坦凝聚是一种特殊的宏观量子现象. 在平均场理论下, 标量玻色-爱因斯坦凝聚可用Gross-Pitaevskii (GP)方程描述, 而旋量玻色-爱因斯坦凝聚则用GP 方程组描述. 非自治GP 方程组被用来研究旋量玻色-爱因斯坦凝聚体的量子操控问题, 其孤子解对于深入理解旋量玻色-爱因斯坦凝聚体的动力学行为具有非常重要的意义. 本文考虑了一类非自治~GP 方程组, 利用非等谱Lax 对得到了其可积性条件, 并在可积情形下构造了方程组解的N-Darboux 变换, 得到了方程组的N-孤子解,以及无穷多个守恒律, 并给出了前三个守恒律的具体表达形式.
Other AbstractBose-Einstein condensate (BEC) is a special kind of macroscopic quantum phenomena. Under the mean field theory, while the scalar BEC is described by the Gross-Pitaevskii (GP) equation, the spinor BEC is described by the coupled Gross-Pitaevskii (GP) system. The nonautonomous GP system is used to study the quantum manipulation in the condensate, its soliton solutions are very helpful for understanding the dynamics of the spinor BEC. In this dissertation, we consider a kind of nonautonomous GP system, with the help of nonisospectral Lax pair, we get the integrability conditions and the N-fold Darboux transformation of the system has been constructed. The N-fold soliton-like solutions and infinite many conservation laws are presented. In particular, the first three conservation laws have been written down explicitly.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225443
Collection数学与统计学院
Recommended Citation
GB/T 7714
郑丹丹. 非自治GP方程组的N-Darboux变换和守恒律[D]. 兰州. 兰州大学,2014.
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