On the derivative nonlinear Schr\"odinger equation with weakly dissipative structure
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derivativedissipativeequationnonlinearodingerschrweaklycondition
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We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equation in one space dimension. Under a suitable weakly dissipative condition on the nonlinearity, we show that the small data solution has a logarithmic time decay in $L^2$.
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