带有外势的聚焦非线性薛定谔方程的近似行波
Approximate traveling waves for the focusing NLS with an external potential
AI总结：
针对受快速衰减外势扰动的三维聚焦三次非线性薛定谔方程构造近似行波解，以此证明在未受扰方程基态阈值以上的任意质量-能量值，都存在向前整体、H¹有界且非散射的解。
AI中文摘要：
我们针对受快速衰减外势扰动的三维聚焦三次非线性薛定谔方程，构造了近似行波解；作为应用，证明了未受扰方程基态阈值以上的任意质量-能量值，都存在向前整体、H¹有界且非散射的解。
英文摘要：
We construct approximate traveling wave solutions for the $3d$ focusing cubic NLS perturbed by a rapidly decaying external potential. As an application, we demonstrate that there exists a forward-global, $H^1$ bounded, nonscattering solution at any mass-energy higher than the ground state threshold for the unperturbed equation.
