On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term
On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term
<p style='text-indent:20px;'>Considered herein is the well-posedness and stability for the Cauchy problem of the fourth-order Schrödinger equation with nonlinear derivative term <inline-formula><tex-math id="M1">\begin{document}$ iu_{t}+\Delta^2 u-u\Delta|u|^2+\lambda|u|^pu = 0 $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ t\in\mathbb{R} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ x\in \mathbb{R}^n $\end{document}</tex-math></inline-formula>. First of all, for initial data <inline-formula><tex-math id="M4">\begin{document}$ \varphi(x)\in H^2(\mathbb{R}^{n}) $\end{document}</tex-math></inline-formula>, …