Rank 2 Bäcklund Transformations of Hyperbolic Monge-Ampère Systems

Abstract

There are two main types of rank 2 Bäcklund transformations relating a pair of hyperbolic Monge-Ampère systems, 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; 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 $\mathcal{B}$ 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.

39 pages

References in corpus (6)

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