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 $L^2$.

10 pages

Cited by in corpus (1)

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