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

Symmetry Integrability and Geometry-Methods and Applications

article

Giorgio Gubbiotti¹  Christian Scimiterna²  Ravil I. Yamilov³ 

[1] School of Mathematics and Statistics, The University of Sydney;Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre and Sezione INFN di Roma Tre;Institute of Mathematics, Ufa Scientific Center, Russian Academy of Sciences

关键词: quad-equations;    Darboux integrability;    exact solutions;    CAC;   

DOI  :  10.3842/SIGMA.2018.008

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown