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.
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页码：1390 / 1403
页数：14
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