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 eq...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.展开更多
基金Supported by the National Natural Science Foundation of China. Grant 19901007.
文摘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.
