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In this work, we prove the existence of wave operator for the followinggeneralized derivative nonlinear Schr\"odinger equation \begin{align*}i\partial_t u+\partial_x^2 u +i |u|^{2\sigma}\partial_x u=0, \end{align*} with$(t,x)\in\mathbb{R}\times\mathbb{R}$, $\sigma\in \mathbb{N}$, and $\sigma\geq3$. The study of wave operators is an important part of the scattering theory,and it is useful in the construction of the nonlinear profile and the largedata scattering.  The previous argument for small data scattering in \cite{BaiWuXue-JDE}, whichis based on the local smoothing effect and maximal function estimates, breaksdown when considering the final data problem. The main reason is that theresolution space does not provide smallness near the infinite time. We overcomethis difficulty by invoking the gauge transformation and the normal formmethod.

Wave operator for the generalized derivative nonlinear Schr\"{o}dinger equation