可积系统
哈密顿量(控制论)
守恒量
边值问题
非线性薛定谔方程
非线性系统
曲率
数学物理
薛定谔方程
物理
数学分析
数学
量子力学
几何学
数学优化
作者
Vincent Caudrelier,Nicolas Crampé,E. Ragoucy,Cheng Zhang
标识
DOI:10.1016/j.physd.2023.133650
摘要
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schr\"odinger equation on the half-line. This is based on the investigation of time-dependent reflection matrices which satisfy the boundary zero curvature equation. In particular, this leads to absorption/emission processes at the boundary that can take place for solitons and higher-order solitons. As a consequence, the usual charges on the half-line are no longer conserved but we show explicitly how to restore an infinite set of conserved quantities by taking the boundary into account. The Hamiltonian description and Poisson structure of the model are presented, which allows us to derive for the first time a classical version of the boundary algebra used originally in the context of the quantum nonlinear Schr\"odinger equation.
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