论文标题
非线性schrödinger方程中的多索顿动力学
Multi-soliton dynamics in the nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，我们研究了非线性schrödinger方程的库奇问题，该方程具有非数字势$ v_ \ varepsilon（x）$。特别是，我们考虑了初始数据接近具有规定阶段和位置的$ k $ solitons并研究Schrödinger系统的演变的情况。 We prove that over a large time interval with the maximum time tending to infinity, all $k$ solitons will maintain the shape, and the solitons dynamics can be regarded as an approximation of $k$ particles moving in $\mathbb{R}^N$ with their accelerations dominated by $\nabla V_\varepsilon$, provided the barycenters of these solitons do not coincide.
In this paper, we study the Cauchy problem of the nonlinear Schrödinger equation with a nontrival potential $V_\varepsilon(x)$. In particular, we consider the case where the initial data is close to a superposition of $k$ solitons with prescribed phase and location, and investigate the evolution of the Schrödinger system. We prove that over a large time interval with the maximum time tending to infinity, all $k$ solitons will maintain the shape, and the solitons dynamics can be regarded as an approximation of $k$ particles moving in $\mathbb{R}^N$ with their accelerations dominated by $\nabla V_\varepsilon$, provided the barycenters of these solitons do not coincide.
