Asymptotic behavior in time of solution to the nonlinear Schr"odinger equation with higher order anisotropic dispersion

Abstract: We consider the asymptotic behavior in time of solutions to the nonlinear Schr"odinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS).