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

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.

34 pages

References in corpus (3)

• Algebraic Entropy for lattice equations
• Darboux Integrability of Trapezoidal $H^4$ and $H^6$ Families of Lattice Equations II: General Solutions
• Linearizability and fake Lax pair for a consistent around the cube nonlinear non-autonomous quad-graph equation

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