| 具阻尼的Gross-Pitaevskii(GP)方程的整体解 |
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| 引用本文： | 张健,舒级,刘妍丽. 具阻尼的Gross-Pitaevskii(GP)方程的整体解[J]. 四川师范大学学报(自然科学版), 2003, 26(5): 441-444 |
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| 作者姓名： | 张健 舒级 刘妍丽 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | :国家自然科学基金 (1 0 2 71 0 84)，四川省杰出青年学科带头人基金资助项目~~ |
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| 摘 要： | 考虑临界的具阻尼的Gross-Pitaevskii(GP)方程iψt=-Δψ+|x|2ψ+g|ψ|4/Dψ+iaψ,t≥0, x∈RD, g＜0, a＜0,这里D是空间维数.这个方程很好地描述了吸引的玻色-爱因斯坦凝聚(BEC).通过偏微分方程的严格理论和变分方法,获得了整体解的一个充分条件,而这个条件利用了非线性数量场方程-Δu+(2)/(b)u-|u|4/Du=0的唯一正解.
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| 关 键 词： | 整体解 阻尼 Gross-Pitaevskii（GP）方程 玻色-爱因斯坦凝聚 BEC 变分方法 |
Global Existence for the Damped Gross-Pitaevskii (GP) Equation |
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| Abstract. Global Existence for the Damped Gross-Pitaevskii (GP) Equation[J]. Journal of Sichuan Normal University(Natural Science), 2003, 26(5): 441-444 |
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| Authors: | Abstract |
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| Abstract: | This paper considers a critical damped Gross-Pitaevskii(GP) equation iψt=-Δψ+|x|2ψ+g|ψ|4/Dψ+iaψ, t≥0, x∈RD, g＜0, a＜0, where D is the space dimension and this equation is well used to describe attractive Bose-Einstein Condensation (BEC). By rigorous theory of partial differential equation and variational arguments, a sufficient condition for global existence is obtained and this condition is in terms of a unique positive solution of nonlinear scalar field equation -Δu+(2)/(D)u-|u|4/Du=0. |
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| Keywords: | Global existence Damped Gross-Pitaevskii(GP) equation Bose-Einstein Condensation (BEC) Variational arguments |
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