ON THE LINEAR WAVE REGIME OF THE GROSS-PITAEVSKII EQUATION

被引：11

作者：

Bethuel, Fabrice ^{[1
]}

Danchin, Raphael ^{[2
]}

Smets, Didier ^{[1
]}

机构：

[1] Univ Paris 06, Lab JL Lions, UMR 7598, F-75013 Paris, France

[2] Univ Paris Est, LAMA, UMR 8050, F-94010 Creteil, France

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2010年 / 110卷

关键词：

NONLINEAR SCHRODINGER-EQUATION; SEMICLASSICAL LIMIT; CAUCHY-PROBLEM; DYNAMICS; INFINITY; DECAY;

D O I：

10.1007/s11854-010-0008-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study long-wavelength asymptotics for the Gross-Pitaevskii equation corresponding to perturbations of a constant state of modulus one. We exhibit lower bounds on the first occurrence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.

引用

页码：297 / 338

页数：42

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