论文标题
半行的非线性schrödinger方程，没有保守数量的孤子
Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
论文作者
论文摘要
我们探索了半线上非线性schrödinger方程的可集成边界吸收/发射的现象。这是基于时间依赖性反射矩阵的研究，该矩阵满足边界零曲率方程。特别是，这会导致在孤子和高阶孤儿可能发生的边界处的吸收/排放过程。结果，半线上的通常的费用不再保守，但我们明确显示了如何通过考虑边界来恢复无限的保守数量。呈现了模型的哈密顿描述和泊松结构，这使我们能够首次得出最初在量子非线性schrödinger方程中最初使用的边界代数的经典版本。
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schrödinger 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 Schrödinger equation.
