ASYMPTOTIC EXPANSION OF SOLUTIONS TO THE NONLINEAR SCHRODINGER EQUATION WITH POWER NONLINEARITY

被引：1

作者：

Masaki, Satoshi ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Sci, Dept Math, Sakyo Ku, Kyoto 6068502, Japan

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2009年 / 63卷 / 01期

关键词：

nonlinear; Schrodinger equation; asymptotic behavior of the solution; asymptotic expansion; SCATTERING-THEORY; HARTREE-EQUATIONS; ENERGY;

D O I：

10.2206/kyushujm.63.51

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study an asymptotic expansion near t = infinity of the solution to the Cauchy problem for the nonlinear Schrodinger equation with repulsive short-range nonlinearity of power type We construct two kinds of approximate solution with asymptotic expansions The first is an accurate approximate solution and of abstract form The second is the approximation of the first and of explicit form The sharpness of these approximations strongly depend on the fractional part of the power of the nonlinearity In particular, if the power is an integer, we obtain a complete expansion of the solution

引用

页码：51 / 82

页数：32

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