In this paper, we obtain the unconditional uniqueness for the rough solutions of the derivative nonlinear Schrödinger equation $$ i\partial_t u + \partial^2_{x} u =i\partial_{x}(|u|^2u) $$ in $C([0,T];H^s(\mathbb R))$, $s\in(\frac{2}{3},1]$. The arguments used here are the normal form argument, resonant decomposition and the Bourgain argument. The main ingredient in the proof is to improve the regularity of the solution by iteration method and finally show that the solution belongs to some Bourgain space.

中文翻译：

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导数非线性Schrödinger方程的粗糙解的规则性和唯一性

在本文中，我们获得了导数非线性Schrödinger方程的粗糙解的无条件唯一性$$ i \ partial_t u + \ partial ^ 2_ {x} u = i \ partial_ {x}（| u | ^ 2u）$$ in $ C（[0，T]; H ^ s（\ mathbb R））$，$ s \ in（\ frac {2} {3}，1] $。这里使用的参数是普通形式的参数，谐振证明和Bourgain参数是证明的主要内容，是通过迭代方法提高解的正则性，最后证明该解属于某个Bourgain空间。