We construct finite positive time blow up solutions for the nonlinear Schrödinger equation with the power nonlinearity whose coefficient is complex number. We also observe that those solutions exist time globally for the negative time. We show a sequence of solutions closes to the blow up profile which is a blow up solution of ODE. We apply the Aubin-Lions lemma for the compactness argument for its convergence.
Shota Kawakami. Shuji Machihara. "Blowup solutions for the nonlinear Schrödinger equation with complex coefficient." Differential Integral Equations 33 (9/10) 445 - 464, September/October 2020. https://doi.org/10.57262/die/1600135321