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arXiv · 1310.2282

Darboux integrable discrete equations possessing an autonomous first-order integral

S. Ya. Startsev
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Abstract

All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is obtained from a subclass of these equation via a non-point transformation. The general proposition on the symmetry structure of the quad-graph equations is proved as an auxiliary result.

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S. Ya. Startsev. 2013-10-08. Darboux integrable discrete equations possessing an autonomous first-order integral. https://doi.org/10.1088/1751-8113/47/10/105204

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