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

Authors
Wang, Bao Xiang
Citation
Wang, Bao Xiang, The Smoothness of Scattering Operators for Sinh-Gordon and Nonlinear Schrdinger Equations, Acta mathematica Sinica. English series (Print) , 18(3), 2002, pp. 549-564
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
18
Issue
3
Year of publication
2002
Pages
549 - 564
Database
ACNP
SICI code
Abstract
We show that the scattering operator carries a band in H s(n) H s1 (n) into H s(n) H s1(n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where sn/2 is arbitrary and n 2. Therefore, the scattering operators are infinitely smooth for the above two equations.