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On the derivative nonlinear Schrödinger equation with weakly dissipative structure (2004.12075v1)
Published 25 Apr 2020 in math.AP
Abstract: 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 $L2$.