In this paper, we investigate a multidimensionally consistent coupled quadrilateral system of the discrete Boussinesq type, proposed by Fordy and Xenitidis recently. It is distinguished from the known discrete Boussinesq type equations by a special dispersion relation. A Bäcklund transformation is constructed and a one-soliton solution is derived using the Bäcklund transformation. We also give bilinear forms of the coupled equations and present formulae for multisoliton solutions. Both plane wave factor and phase factor in two-soliton solutions indicate the coupled systems belong to the discrete Boussinesq family, but there is no continuous correspondence in terms of the Miwa coordinates.

在本文中，我们研究了 Fordy 和 Xenitidis 最近提出的离散 Boussinesq 类型的多维一致耦合四边形系统。它通过特殊的色散关系与已知的离散 Boussinesq 型方程区分开来。构造 Bäcklund 变换并使用 Bäcklund 变换导出单孤子解。我们还给出了耦合方程的双线性形式，并给出了多孤子解的公式。双孤子解中的平面波因子和相位因子都表明耦合系统属于离散 Boussinesq 族，但在 Miwa 坐标上没有连续的对应关系。