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arXiv · 1608.03506

Darboux integrability of trapezoidal $H^{4}$ and $H^{6}$ families of lattice equations I: First integrals

G. Gubbiotti·R. I. Yamilov
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Abstract

In this paper we prove that the trapezoidal $H^{4}$ and the $H^{6}$ families of quad-equations are Darboux integrable systems. This result sheds light on the fact that such equations are linearizable as it was proved using the Algebraic Entropy test [G. Gubbiotti, C. Scimiterna and D. Levi, Algebraic entropy, symmetries and linearization for quad equations consistent on the cube, \emph{J. Nonlinear Math. Phys.}, 23(4):507543, 2016]. We conclude with some suggestions on how first integrals can be used to obtain general solutions.

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G. Gubbiotti, R. I. Yamilov. 2017-02-20. Darboux integrability of trapezoidal $H^{4}$ and $H^{6}$ families of lattice equations I: First integrals. https://doi.org/10.1088/1751-8121%2Faa7fd9

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