Abstract
We study an asymptotic expansion near t=∞ of the solution to the Cauchy problem for the nonlinear Schrödinger equation with repulsive short-range nonlinearity of power type. We construct two kinds of approximate solution with asymptotic expansions. The first is an accurate approximate solution and of abstract form. The second is the approximation of the first and of explicit form. The sharpness of these approximations strongly depend on the fractional part of the power of the nonlinearity. In particular, if the power is an integer, we obtain a complete expansion of the solution.
