SOLUTIONS TO NONLINEAR HIGHER ORDER SCHRODINGER EQUATIONS WITH SMALL INITIAL DATA ON MODULATION SPACES

In this paper, we consider the Cauchy problem for the non-linear higher order Schrodinger equations on modulation spaces M-p,q(s) and show the existence of a unique global solution by using integrability of time decay factors of time decay estimates. As a result, we are able to deal with wider classes of a nonlinearity and a solution space. Moreover, we study time decay estimates of a semi group e(it phi(root-Delta/)) with a polynomial symbol phi. Considering multiplicities of critical points and inflection points of phi carefully, we have time decay estimates with better time decay rate.