Long-time asymptotic behavior of a mixed schrödinger equation with weighted Sobolev initial data

Qiaoyuan Cheng, Yiling Yang, Engui Fan

We apply $\bar{\partial }$ steepest descent method to obtain sharp asymptotics for a mixed schrödinger equation $$q_t+i{q}_{xx}-ia(|q{|}^{2}q{)}_x-2b^2|q{|}^{2}q=0,$$ $$q…