论文标题
具有潜在的非义型NLS激发孤子的全局动力学
Global dynamics below excited solitons for the non-radial NLS with potential
论文作者
论文摘要
在存在外部电位的情况下，我们考虑了$ 3D $立方非线性schrödinger方程的解决方案的全球动力，在方程式在小质量下均可接受基态孤子和激发孤子的情况。我们证明，低于激发孔的能量的小型质量解决方案要么散射到地面状态，要么在时间上生长其$ h^1 $ norm。特别是，我们将Nakanishi [19]的结果从径向延伸到非radial环境。
We consider the global dynamics of solutions to the $3d$ cubic nonlinear Schrödinger equation in the presence of an external potential, in the setting in which the equation admits both ground state solitons and excited solitons at small mass. We prove that small mass solutions with energy below that of the excited solitons either scatter to the ground states or grow their $H^1$-norm in time. In particular, we give an extension of the result of Nakanishi [19] from the radial to the non-radial setting.
