Geodesic
Construction of localized particular solutions of chains with three independent variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 291-301

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We consider differential–difference chains with three independent variables of the form $u^j_{n+1,x} = F(u^j_{n,x}, u^{j+1}_n, u^j_n, u^j_{n+1}, u^{j-1}_{n+1})$. An effective approach to the study and classification of equations with three independent variables is the method based on Darboux-integrable reductions. Using the Darboux-integrable reductions, we construct localized particular solutions of chains with three independent variables.
Keywords: three-dimensional chains, characteristic algebras, Darboux integrability, characteristic integrals, integrable reductions. 
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     author = {M. N. Kuznetsova},
     title = {Construction of localized particular solutions of chains with three independent variables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {291--301},
     publisher = {mathdoc},
     volume = {216},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a6/}
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M. N. Kuznetsova. Construction of localized particular solutions of chains with three independent variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 291-301. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a6/