This paper is a continuation of our previous study  on the long time behavior of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, for a given asymptotic profile u+, we construct a solution to (4NLS) which converges to u+ as t→∞, where u+ is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction.
All Science Journal Classification (ASJC) codes
- Applied Mathematics