# A particular solution of cubic Szegö equation.

Consider the projection operator $$\Pi\left(\sum_{k\in \mathbb{Z}}\hat{f}(k)e^{ikx}\right)= \sum_{k>0}\hat{f}(k)e^{ikx},$$ where $\hat{f}(k)=\frac{1}{2\pi}\int_{0}^{2\pi}f(x)e^{-ikx}dx$. Then consider the Szegö equation: $$i\frac{d}{dt}u= \Pi\left(u|u|^2\right).$$ I would like to know if there is a solution of the form: $$u(t,x)=\frac{a(t)}{1-c(t)e^{ix}}.$$

I apologize if the question is too vague.

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