An auto-Bcklund transformation for the quad equation Q1₁ is considered as a discrete equation, called H2 ^a , which is a so called torqued version of H2. The equations H2 ^a and Q1₁ compose a consistent cube, from which an auto-Bcklund transformation and a Lax pair for H2 ^a are obtained. More generally it is shown that auto-Bcklund transformations admit auto-Bcklund transformations. Using the auto-Bcklund transformation for H2 ^a we derive a seed solution and a one-soliton solution. From this solution it is seen that H2 ^a is a semi-autonomous lattice equation, as the spacing parameter q depends on m but it disappears from the plane wave factor.

四元方程Q1 ₁的自动Bcklund 变换被视为离散方程，称为H2 ^a，它是H2^的所谓扭矩版本。方程H2 ^a和Q1 ₁组成了一个一致的立方体，从中得到了H2 ^a的自动Bcklund 变换和Lax 对。更普遍地表明，自动Bcklund 变换允许自动Bcklund 变换。使用 H2 ^a的 auto-Bcklund 变换，我们推导出种子解和单孤子解。从这个解可以看出 H2 ^a是一个半自治的格子方程，因为间距参数q取决于m 但它从平面波因子中消失了。