Time-like boundary conditions in the NLS model
Time-like boundary conditions in the NLS model
复制标题
NLS 模型中的类时边界条件
DOI：
10.1016/j.nuclphysb.2019.02.022
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发表时间：
2019
影响因子：
2.8
通讯作者：
S. Sklaveniti
中科院分区：
文献类型：
--
作者：
A. Doikou;Iain Findlay;S. Sklaveniti
我们关注非线性薛定谔模型，并在存在可积类时边界条件的情况下扩展时空对偶性的概念。我们确定了相关的类时“守恒”量和 Lax 对以及相应的边界条件。特别是，在由反射方程的解定义的类时边界的情况下，我们推导了 Lax 对的空间分量的生成函数。边界 Lax 对上的解析条件导致类似时间的边界条件。类似时间的装饰也是第一次进行，作为产生相关层次结构的宽松对的空间成分的有效手段。在缺乏经典矩阵的情况下，或者在考虑复杂的基础代数结构时，这一点尤其重要。还导出了相关的时间 Riccati 方程以及类时守恒量。为此，我们使用矩阵 NLS 类型层次结构作为主要范例。
We focus on the non-linear Schrödinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions. We identify the associated time-like “conserved” quantities and Lax pairs as well as the corresponding boundary conditions. In particular, we derive the generating function of the space components of the Lax pairs in the case of time-like boundaries defined by solutions of the reflection equation. Analytical conditions on the boundary Lax pair lead to the time like-boundary conditions. The time-like dressing is also performed for the first time, as an effective means to produce the space components of the Lax pair of the associated hierarchy. This is particularly relevant in the absence of a classicalr-matrix, or when considering complicated underlying algebraic structures. The associated time Riccati equations and hence the time-like conserved quantities are also derived. We use as the main paradigm for this purpose the matrix NLS-type hierarchy.