Darboux Integrability of Trapezoidal $H^4$ and $H^6$ Families of Lattice Equations II: General Solutions

Abstract

In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal $H^4$ equations and the $H^6$ equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages, arXiv:1608.03506]. These first integrals are used to reduce the problem to the solution of some linear or linearizable non-autonomous ordinary difference equations which can be formally solved.

References in corpus (2)

• Darboux integrability of trapezoidal $H^4$ and $H^6$ families of lattice equations I: First integrals
• Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation

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• Algebraic entropy for hex systems
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