Article
Ufa Mathematical Journal
Volume 4, Number 3, pp. 174-180
Examples of Darboux Integrable Discrete Equations Possessing First Integrals of an Arbitrarily High Minimal Order
Garifullin R.N., Yamilov R.I.
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We consider a discrete equation, defined on the two-dimensional square lattice, which is linearizable, namely, of the Burgers type and depends on a parameter $\alpha$. For any natural number $N$ we choose $\alpha$ so that the equation becomes Darboux integrable and the minimal orders of its first integrals in both directions are greater or equal than $N$.