Abstract
We show that the scattering operator carries a band in Hs(ℝn) ×Hs−1 (ℝn) into Hs(ℝn) ×Hs−1(ℝn) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrodinger 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.
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