Title: Soliton-potential interactions for nonlinear Schrödinger equation in $\mathbb{R}^3$,
Abstract: In this work we mainly consider the dynamics and scattering of a narrow
soliton of NLS equation with a potential in $\mathbb{R}^3$, where the
asymptotic state of the system can be far from the initial state in parameter
space. Specifically, if we let a narrow soliton state with initial velocity
$\upsilon_{0}$ to interact with an extra potential $V(x)$, then the velocity
$\upsilon_{+}$ of outgoing solitary wave in infinite time will in general be
very different from $\upsilon_{0}$. In contrast to our present work, previous
works proved that the soliton is asymptotically stable under the assumption
that $\upsilon_{+}$ stays close to $\upsilon_{0}$ in a certain manner.