The Smoothness of Scattering Operators for Sinh-Gordon and Nonlinear Schrodinger Equations

作     者：Bao Xiang WANG Department of Mathematics, Hebei University. Baoding 071002. P. R. China 

作者机构：Department of Mathematics Hebei University Baoding P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2002年第18卷第3期

页      面：549-564页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China. Grant 19901007 

主　　题：Sinh-Gordon equation Nolinear Schrodinger equation The smoothness of scattering operator 

摘      要：We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where s≥n/2 is arbitrary and n≥2. Therefore, the scattering operators are infinitely smooth for the above two equations.