On the derivative nonlinear Schrödinger equation with weakly dissipative structure

Abstract

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 $L^2$.

arXiv comment10 pages

References in corpus (6)

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Cited by in corpus (1)

• On the decay estimate for small solutions to nonlinear Klein-Gordon equations with dissipative structure