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2002 The global Cauchy problem and scattering of solutions for nonlinear Schrödinger equations in $H^s$
Boling Guo, Baoxiang Wang
Differential Integral Equations 15(9): 1073-1083 (2002).

Abstract

In this paper, we shall prove that the scattering operator for nonlinear Schr\"{o}dinger equations $ iu_t+(-\Delta)^m u=\lambda_1|u|^{p_1}u+ \lambda_2|u|^{p_2}u$ carries a band $\dot B(p_1,p_2,\delta)$ in $H^s$ into $H^s$ for some $\delta>0$, where $\dot B(p_1,p_2,\delta)=\{\varphi\in H^s: \|\varphi\|_{\dot H^{s(p_1)}\cap\dot H^{s(p_2)}}\leq \delta\}$, $s(p_i)=n/2-2m/p_i$, $s(p_2)\leq s\le s(p_1)+1$, $4m/n\leq p_1\leq p_2\leq 4m/(n-2s)$.

Citation

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Boling Guo. Baoxiang Wang. "The global Cauchy problem and scattering of solutions for nonlinear Schrödinger equations in $H^s$." Differential Integral Equations 15 (9) 1073 - 1083, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1161.35502
MathSciNet: MR1919763

Subjects:
Primary: 35Q55
Secondary: 35P25

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 9 • 2002
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