Geodesic
On one integrable discrete system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 140 (2017), pp. 30-42.

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In this paper, we study a system of nonlinear equations on a square graph related to the affine algebra $A^{(1)}_1$. This system is the simplest representative of the class of discrete systems corresponding to affine Lie algebras. We find the Lax representation and construct hierarchies of higher symmetries. In neighborhoods of singular points $\lambda=0$ and $\lambda=\infty$, we construct formal asymptotic expansions of eigenfunctions of the Lax pair and, based on these expansions, find series of local conservation laws for the system considered.
Mots-clés : Lax pair
Keywords: higher symmetry, conservation law, recursion operator, formal diagonalization. 
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     author = {E. V. Pavlova and I. T. Habibullin and A. R. Khakimova},
     title = {On one integrable discrete system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {30--42},
     publisher = {mathdoc},
     volume = {140},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_140_a2/}
}
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E. V. Pavlova; I. T. Habibullin; A. R. Khakimova. On one integrable discrete system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 140 (2017), pp. 30-42. http://geodesic.mathdoc.fr/item/INTO_2017_140_a2/