孤立子在外部势场中的能量冻结
Freezing of energy of a soliton in an external potential
摘要：
本文研究了具有小的Schwartz类外势$εV$的广义非线性系统中孤子的动力学。我们证明了存在一个描述孤子动力学的有效力学系统，并且对于任何正整数$r$，这样的力学系统的能量几乎守恒到$ε^{-r}$阶的倍。在旋转不变的情况下，我们推导出的孤子的真实轨道仍然接近机械的一个到倍的顺序$ε^{-r}$。
英文摘要：
In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential $εV$ of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer $r$, the energy of such a mechanical system is almost conserved up to times of order $ε^{-r}$. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order $ε^{-r}$.
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