论文标题
等级2Bäcklund的双曲线蒙格 - 安培系统的转换
Rank 2 Bäcklund Transformations of Hyperbolic Monge-Ampère Systems
论文作者
论文摘要
等级2Bäcklund转换有两种主要类型，与一对双曲线Monge-Ampère系统相关，我们称其为type $ \ mathscr {a} $和type $ \ mathscr {b} $。对于类型$ \ MATHSCR {a} $，我们完全确定了一个子类，其本地不变性满足特定但简单的代数约束；这种Bäcklund转换是通过有限数量的常数来参数的，其同构性可以为2、3或4。此外，我们提出了一种不变的条件，该条件确定了一个通用类型$ \ Mathscr {b} $bäcklund转换是否是一种$ Z = $ Z的适当选择。 f（x，y，z，z_x，z_y）$，并保留解决方案上的$ x，y $变量。
There are two main types of rank 2 Bäcklund transformations relating a pair of hyperbolic Monge-Ampère systems, which we call Type $\mathscr{A}$ and Type $\mathscr{B}$. For Type $\mathscr{A}$, we completely determine a subclass whose local invariants satisfy a specific but simple algebraic constraint; such Bäcklund transformations are parametrized by a finite number of constants, whose cohomogeneity can be either 2, 3 or 4. In addition, we present an invariantly formulated condition that determines whether a generic Type $\mathscr{B}$ 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.
