
arXiv: 1106.0636
We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B��cklund transformations. At least one of the members of each family is integrable, hence the whole family inherits some integrability properties.
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Yang-Baxter maps, 82B20, 37K35, 39A05, FOS: Physical sciences, Mathematical Physics (math-ph), Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, consistency around the cube, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, QA1-939, Exactly Solvable and Integrable Systems (nlin.SI), General theory of difference equations, Mathematics, Mathematical Physics, integrable lattice equations
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Yang-Baxter maps, 82B20, 37K35, 39A05, FOS: Physical sciences, Mathematical Physics (math-ph), Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, consistency around the cube, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, QA1-939, Exactly Solvable and Integrable Systems (nlin.SI), General theory of difference equations, Mathematics, Mathematical Physics, integrable lattice equations
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