| Abstract: |
| We consider asymptotic behavior of small solutions to a one-dimensional nonlinear Schr\{o}dinger equation with a non-local cubic derivative nonlinear term, which has dissipative effect. In the periodic setting, dissipation becomes prominent and the initial value problem is known to be ill-posed backward in time even for small data. In contrast, on the real line we show global existence of solutions and modified scattering behavior in both time directions for small data in weighted Sobolev space. |
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