Searching for integrable lattice maps using factorization

Details Searching for integrable lattice maps using factorization Searching for integrable lattice maps using factorization

2007-05-14

arxiv.org/abs/0705.1903v2

J. Phys. A: Math. Theor. 40 (2007) 12629

Nonlinear Sciences

Exactly Solvable and Integrable Systems

To appear in Journal of Physics A. Some changes in references

Scientific paper

10.1088/1751-8113/40/42/S09

We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of iteration. The results were then classified using algebraic entropy. Some new models with polynomial growth (strongly associated with integrability) were found. One of them is a nonsymmetric generalization of the homogeneous quadratic maps associated with KdV (modified and Schwarzian), for this new model we have also verified the "consistency around a cube".

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