论文标题
有限长度涡流丝及其应用的Hasimoto转换
The Hasimoto Transformation for a Finite Length Vortex Filament and its Application
论文作者
论文摘要
我们考虑两个非线性方程，分别是局部诱导方程和立方非线性schrödinger方程，并证明每个方程的某些初始值问题的可溶性是通过广义的Hasimoto变换等效的。作为一种应用，我们证明了基于作者在准备中，作者在准备中，基于对局部诱导方程获得的稳定性估计值的非线性schrödinger方程的轨道稳定性。据作者所知，这是对本地归纳方程的分析以及Hasimoto转换的第一次，为非线性Schrödinger方程提供了新的见解。
We consider two nonlinear equations, the Localized Induction Equation and the cubic nonlinear Schrödinger Equation, and prove that the solvability of certain initial-boundary value problems for each equation is equivalent through the generalized Hasimoto transformation. As an application, we prove the orbital stability of plane wave solutions of the nonlinear Schrödinger equation based on stability estimates obtained for the Localized Induction Equation by the author in a paper in preparation. As far as the author knows, this is the first time that the analysis of the Localized Induction Equation, along with the Hasimoto transformation, provided new insight for the nonlinear Schrödinger equation.
