We find the asymptotic behavior for large time of solutions to the dispersive equations of Schrödinger type where . We obtain some estimates of solutions of linear problem and apply them to nonlinear problems with power nonlinearities of order . The nonexistence of wave operator and existence of the modified wave operator for the critical nonlinearity are studied.
Nakao HAYASHI. Pavel I. NAUMKIN. "Asymptotic properties of solutions to dispersive equation of Schrödinger type." J. Math. Soc. Japan 60 (3) 631 - 652, July, 2008. https://doi.org/10.2969/jmsj/06030631