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This paper is a continuation of our previous study on the long time behaviorof solution to the nonlinear Schr"odinger equation with higher orderanisotropic dispersion (4NLS). We prove the long range scattering for (4NLS)with the quadratic nonlinearity in two dimensions. More precisely, for a givenasymptotic profile $u_{+}$, we construct a solution to (4NLS) which convergesto $u_{+}$ as t to infinity, where $u_{+}$ is given by the leading term of thesolution to the linearized equation of (4NLS) with a logarithmic phasecorrection.

Long range scattering for the nonlinear Schr"odinger equation with higher order anisotropic dispersion in two dimensions