Examples of Darboux Integrable Discrete Equations Possessing First Integrals of an Arbitrarily High Minimal Order

2012/07/12 by Garifullin, Rustem N., Yamilov, Ravil I.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.1207.2895

Abstract

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 α. For any natural number N we choose α so that the equation becomes Darboux integrable and the minimal orders of its first integrals in both directions are greater or equal than N.

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