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# Modulation Spaces and Schr"odinger Equation

It is known that NLS(nonlinear Schr\"odinger equation) is locally well-posed in modulation spaces for the power-type nonlinearity $u|u|^{\alpha}, \alpha \in 2 \mathbb N.$ As an application to composition operators on the modulation spaces, we point out that the standard method for the evolution of NLS cannot be considered for the power-type nonlinearity $|u|^{\alpha}u, \alpha \in (0, \infty) \setminus 2 \mathbb N.$ We study the Cauchy problem for the HTE with a Cauchy data in modulation spaces, and obtain local and global well-posedness results for the HTE.