Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-06-12
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages v1: original version; v2: one equation's conservation laws are simplified; v3: a further minor simplification
Scientific paper
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in order to find candidates for integrability. It turns out that all such candidates have an equivalent affine form. These are tested by calculating their algebraic entropy. In this way, we have found several types of integrable equations, one of which seems to be entirely unrelated to any known discrete integrable system. We also list all single-tile conservation laws for the integrable equations in the above class.
Hydon Peter E.
Viallet Claude-M.
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