On the new critical exponent for the nonlinear Schredinger equations
On the new critical exponent for the nonlinear Schredinger equations
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关于非线性薛定谔方程的新临界指数
DOI：
10.1007/s00030-013-0252-z
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
N.Hayashi and P. Naumkin
中科院分区：
文献类型：
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作者：
Shuji Machihara;Tohru Ozawa and Hidemitsu Wadade;N.Hayashi and P. Naumkin
本文考虑一维p阶非线性薛定谔方程的Cauchy问题（给出公式）。其中（公式表示）。我们揭示了p= 4是一个新的临界指数的大时间渐近行为的解决方案。我们证明了当ps < p< 4时，解的大时间渐近性与线性情形的大时间渐近性有本质的不同，而当p> 4时，解的大时间渐近性具有拟线性性质.
We consider the Cauchy problem for the pth order nonlinear Schrödinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p= 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if p s< p< 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p> 4.