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| We are interested in exact solutions for the derivative nonlinear Schr\"{o}dinger equation with periodic boundary condition. We investigate solutions $u(x,t)={\rm e}^{-i \omega t}\phi (x-ct)$ with $\omega \in {\bf R}$ and $c \in {\bf R}$. The equation is reduced to the nonlocal nonlinear second order differential equation by introducing the polar coordinate. We will talk about representation theorem and the global structure for the equation. |
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