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arXiv · 1904.02827

Geometry of B\"acklund Transformations II: Monge-Amp\`ere Invariants

Yuhao Hu
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Abstract

This article is concerned with the question: For which pairs of hyperbolic Euler-Lagrange systems in the plane does there exist a rank-$1$ B\"acklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler-Lagrange systems. In addition, we discover a class of B\"acklund transformations relating two hyperbolic Euler-Lagrange systems of distinct types.

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Yuhao Hu. 2019-04-04. Geometry of B\"acklund Transformations II: Monge-Amp\`ere Invariants. https://doi.org/10.1093/integr%2Fxyz011

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