Global existence of small solutions to the quadratic nonlinear Schrodinger equations in two space dimensions

被引：4

作者：

Hayashi, N

Naumkin, PI

机构：

[1] Tokyo Univ Sci, Dept Appl Math, Tokyo 1628601, Japan

[2] Univ Michoacana, Inst Fis & Matemat, Morelia 58040, Michoacan, Mexico

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2001年 / 32卷 / 06期

关键词：

nonlinear Schrodinger equations; global existence; quadratic nonlinearities; two spatial dimensions;

D O I：

10.1137/S0036141000372532

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a global existence in time of small solutions to the quadratic nonlinear Schrodinger equation in two space dimensions, (0.1) [GRAPHICS] where [GRAPHICS] lambda (j)k, mu (j)k is an element of C. We prove that if the initial data u 0 satisfy some analyticity and smallness conditions in a suitable norm, then the solution of the Cauchy problem (0.1) exists globally in time. Furthermore we prove the existence of the usual scattering states.

引用

页码：1390 / 1403

页数：14

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