首页|Rank 2 Backlund transformations of hyperbolic Monge-Ampere systems
Rank 2 Backlund transformations of hyperbolic Monge-Ampere systems
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NSTL
Elsevier
This article studies rank 2 Backlund transformations of hyperbolic Monge-Ampere systems using Cartan's method of equivalence. Such Backlund transformations have two main types, which we call Type A and Type B. For Type A, we completely determine a subclass whose local invariants satisfy a specific but simple algebraic constraint. We show that such Backlund 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 B, we present an invariantly formulated condition that determines whether a Backlund 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. (C) 2021 Elsevier B.V. All rights reserved.
Backlund transformationsHyperbolic Monge-Ampere systemsExterior differential systemsCartan's method of equivalence
NSTL
Elsevier
