In this work, we attempt to construct the Lax connections of -deformed integrable field theories in two different ways. With reasonable assumptions, we make an ansatz and find the Lax pairs in the -deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This method is straightforward, but it may be difficult to apply for general models. We then make use of a dynamic coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models and find consistency with those determined using the first method.

在这项工作中，我们试图以两种不同的方式构建变形可积场论的松散联系。在合理的假设下，我们通过直接求解 Lax 方程，进行了 ansatz 并找到了变形仿射 Toda 理论和主手征模型中的 Lax 对。这种方法简单明了，但可能很难应用于通用模型。然后我们利用动态坐标变换从未变形的理论中读取变形理论中的 Lax 连接。我们发现，一旦变换的逆可用，就可以轻松读取 Lax 连接。我们明确展示了几类标量模型的构造，并找到了与使用第一种方法确定的那些模型的一致性。