ASYMPTOTIC EXPANSION OF SOLUTIONS TOTHE NONLINEAR SCHRODINGER EQUATIONWITH POWER NONLINEARITY

摘要

We study an asymptotic expansion near t = Do of the solution to the Cauchyproblem for the nonlinear Schrodinger equation with repulsive short-range nonlinearity ofpower 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 theapproximation of the first and of explicit form. The sharpness of these approximationsstrongly depend on the fractional part of the power of the nonlinearity. In particular, if thepower is an integer, we obtain a complete expansion of the solution.