Darboux Integrability of Trapezoidal H4 and H6 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]. 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.
- Publication:
-
SIGMA
- Pub Date:
- February 2018
- DOI:
- 10.3842/SIGMA.2018.008
- arXiv:
- arXiv:1704.05805
- Bibcode:
- 2018SIGMA..14..008G
- Keywords:
-
- quad-equations; Darboux integrability; exact solutions; CAC;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- SIGMA 14 (2018), 008, 51 pages