This article studies rank 2 Bäcklund transformations of hyperbolic Monge-Ampère systems using Cartan's method of equivalence. Such Bäcklund transformations have two main types, which we call Type $\mathcal{A}$ and Type $\mathcal{B}$. For Type $\mathcal{A}$, we completely determine a subclass whose local invariants satisfy a specific but simple algebraic constraint. We show that such Bäcklund transformations are parametrized by a finite number of constants; in a subcase of maximal symmetry, we determine the coordinate form of the underlying PDEs, which turn out to be Darboux integrable. For Type $\mathcal{B}$, we present an invariantly formulated condition that determines whether a Bäcklund transformation is one that, under suitable choices of local coordinates, relates solutions of two PDEs of the form $z_{xy}=F(x,y,z,z_x,z_y)$ and preserves the $x,y$ variables on solutions.

本文使用 Cartan 的等价方法研究了双曲线 Monge-Ampère 系统的 2 阶 Bäcklund 变换。这种 Bäcklund 变换有两种主要类型，我们称之为 Type$\mathcal{一种}$ 和类型 $\mathcal{乙}$. 类型$\mathcal{一种}$，我们完全确定了一个子类，其局部不变量满足特定但简单的代数约束。我们证明了这种 Bäcklund 变换是由有限数量的常数参数化的；在最大对称的子情况下，我们确定底层偏微分方程的坐标形式，结果证明它是 Darboux 可积的。类型$\mathcal{乙}$，我们提出了一个不变公式化的条件，该条件确定 Bäcklund 变换是否是在适当的局部坐标选择下，将两个 PDE 形式的解相关联的条件 $z_{X是}=F(X,是,z,z_X,z_{是})$ 并保留了 $X,是$ 解决方案的变量。