We consider the initial value problem for cubic derivative nonlinear Schrödinger 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 \(L^2\).

中文翻译：

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关于具有弱耗散结构的导数非线性Schrödinger方程

我们考虑在一维空间中三次导数非线性Schrödinger方程的初值问题。在非线性的适当弱耗散条件下，我们证明了小数据解在\（L ^ 2 \）中具有对数时间衰减。