Asymptotics in time for nonlinear nonlocal Schrödinger equations with a source. (English) Zbl 0927.35109

Summary: We consider the asymptotic behavior of the solution of the Cauchy problem for the nonlinear nonlocal Schrödinger equation (NNS) with a source \[ iu_t+| u|^2u+ iKu= f(x,t),\quad t>0,\quad x\in\mathbb{R}, \]
\[ u(x,0)= \overline u(x). \] Here the linear pseudodifferential operator \(Ku\) is defined by \[ Ku={1\over 2\pi} \int_{\mathbb{R}} e^{ipx}K(p)\widehat u(p,t)dp. \] The source in the NNS equation makes essential alterations to the asymptotic behavior. We study the cases of both small and large initial data.


35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
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