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Construction of localized particular solutions of chains with three independent variables

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Abstract

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.

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Acknowledgments

The author is thankful to I. T. Habibullin for the problem statement and the useful discussions.

Funding

This work was supported by the Russian Science Foundation under grant No. 21-11-00006, https://rscf.ru/en/project/21-11-00006/.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, Russia

    M. N. Kuznetsova

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  1. M. N. Kuznetsova
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Correspondence to M. N. Kuznetsova.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 216, pp. 291–301 https://doi.org/10.4213/tmf10496.

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Kuznetsova, M.N. Construction of localized particular solutions of chains with three independent variables. Theor Math Phys 216, 1158–1167 (2023). https://doi.org/10.1134/S004057792308007X

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  • DOI: https://doi.org/10.1134/S004057792308007X

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