Partial Mass Dynamics of the Defocusing Nonlinear Schrödinger Equation

ABSTRACT We study the long‐time dynamics of the defocusing nonlinear Schrödinger (NLS) equation. Compared with previous literature, we revisit the direct and inverse scattering map to obtain asymptotics in some weighted energy space that requires less restrictive decay and regularity assumptions. The main result is derived from an application of uniform resolvent bound and an approximation argument in the spirit of Riemann–Lebesgue lemma. As a consequence, our result demonstrates that zeros of the solution to the defocusing NLS equation cannot lie in bounded sets as .