论文标题
Davey-Stewartson系统和$（2+1）$ - 尺寸Yajima-oikawa系统的可集成半脱粒化。 ii
Integrable semi-discretizations of the Davey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system. II
论文作者
论文摘要
这是我们以前的论文Arxiv：1904.07924的延续，该论文致力于构建Davey-Stewartson系统的可集成半差异，以及$（2+1）$ - 尺寸Yajima-oikawa系统；在这一系列论文中，我们将两个空间变量之一的离散化视为半差异化。在本文中，我们构建了一个可集成的半混凝土Davey-Stewartson系统，该系统与上一篇论文ARXIV中提出的半混凝土Davey-Stewartson系统基本不同。我们首先通过构造其松弛对象的表示，并表明这两个基本流量通勤与连续的情况一样，我们首先获得了两个基本流的可集成半散制，它们可以通过构成Davey-Stewartson系统。然后，我们考虑两个基本流量的线性组合，以获得Davey-Stewartson系统的新的可集成半差异化。 Using a linear transformation of the continuous independent variables, one of the two elementary Davey-Stewartson flows can be identified with an integrable semi-discretization of the $(2+1)$-dimensional Yajima-Oikawa system proposed in https://link.aps.org/doi/10.1103/PhysRevE.91.062902 .
This is a continuation of our previous paper arXiv:1904.07924, which is devoted to the construction of integrable semi-discretizations of the Davey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system; in this series of papers, we refer to a discretization of one of the two spatial variables as a semi-discretization. In this paper, we construct an integrable semi-discrete Davey-Stewartson system, which is essentially different from the semi-discrete Davey-Stewartson system proposed in the previous paper arXiv:1904.07924. We first obtain integrable semi-discretizations of the two elementary flows that compose the Davey-Stewartson system by constructing their Lax-pair representations and show that these two elementary flows commute as in the continuous case. Then, we consider a linear combination of the two elementary flows to obtain a new integrable semi-discretization of the Davey-Stewartson system. Using a linear transformation of the continuous independent variables, one of the two elementary Davey-Stewartson flows can be identified with an integrable semi-discretization of the $(2+1)$-dimensional Yajima-Oikawa system proposed in https://link.aps.org/doi/10.1103/PhysRevE.91.062902 .
