四川师范大学学报(自然科学版)
四川師範大學學報(自然科學版)
사천사범대학학보(자연과학판)
JOURNAL OF SICHUAN NORMAL UNIVERSITY(Natural Science)
2003年
5期
441-444
,共4页
整体解%阻尼%Gross-Pitaevskii(GP)方程%玻色-爱因斯坦凝聚(BEC)%变分方法
整體解%阻尼%Gross-Pitaevskii(GP)方程%玻色-愛因斯坦凝聚(BEC)%變分方法
정체해%조니%Gross-Pitaevskii(GP)방정%파색-애인사탄응취(BEC)%변분방법
Global existence%Damped%Gross-Pitaevskii(GP) equation%Bose-Einstein Condensation (BEC)%Variational arguments
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.
攷慮臨界的具阻尼的Gross-Pitaevskii(GP)方程iψt=-Δψ+|x|2ψ+g|ψ|4/Dψ+iaψ, t≥0, x∈RD, g＜0, a＜0,這裏D是空間維數.這箇方程很好地描述瞭吸引的玻色-愛因斯坦凝聚(BEC).通過偏微分方程的嚴格理論和變分方法,穫得瞭整體解的一箇充分條件,而這箇條件利用瞭非線性數量場方程-Δu+(2)/(b)u-|u|4/Du=0的唯一正解.
고필림계적구조니적Gross-Pitaevskii(GP)방정iψt=-Δψ+|x|2ψ+g|ψ|4/Dψ+iaψ, t≥0, x∈RD, g＜0, a＜0,저리D시공간유수.저개방정흔호지묘술료흡인적파색-애인사탄응취(BEC).통과편미분방정적엄격이론화변분방법,획득료정체해적일개충분조건,이저개조건이용료비선성수량장방정-Δu+(2)/(b)u-|u|4/Du=0적유일정해.
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.
