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.

中文翻译：

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具有复系数的非线性Schrödinger方程的爆破解。

我们针对系数为复数的幂次非线性的非线性Schrödinger方程，构造了有限的正时间爆破解。我们还观察到，这些解决方案在全球范围内的时间都是负数。我们显示了一系列接近爆破轮廓的解，这是ODE的爆破解决方案。我们将Aubin-Lions引理用于紧致性论证，以求收敛。