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Multidimensional conservation laws and integrable systems II. / Makridin, Zakhar V.; Pavlov, Maxim V.

In: Studies in Applied Mathematics, Vol. 148, No. 2, 02.2022, p. 813-824.

Research output: Contribution to journal › Article › peer-review

Harvard

Makridin, ZV & Pavlov, MV 2022, 'Multidimensional conservation laws and integrable systems II', Studies in Applied Mathematics, vol. 148, no. 2, pp. 813-824. https://doi.org/10.1111/sapm.12460

APA

Makridin, Z. V., & Pavlov, M. V. (2022). Multidimensional conservation laws and integrable systems II. Studies in Applied Mathematics, 148(2), 813-824. https://doi.org/10.1111/sapm.12460

Vancouver

Makridin ZV, Pavlov MV. Multidimensional conservation laws and integrable systems II. Studies in Applied Mathematics. 2022 Feb;148(2):813-824. doi: 10.1111/sapm.12460

Author

Makridin, Zakhar V. ; Pavlov, Maxim V. / Multidimensional conservation laws and integrable systems II. In: Studies in Applied Mathematics. 2022 ; Vol. 148, No. 2. pp. 813-824.

BibTeX

@article{455337b856ab4cbbb9b43330c66b649d,
title = "Multidimensional conservation laws and integrable systems II",
abstract = "In this paper we continue investigation of a new property of two-dimensional integrable systems—existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Multicomponent two-dimensional hydrodynamic reductions of the Mikhal{\"e}v equation are considered. Infinitely many three-dimensional local conservation laws for the Korteweg–de Vries pair of commuting flows are constructed. Thus, we show that pairs of commuting dispersive two-dimensional systems also possess infinitely many local three-dimensional conservation laws. They can be used for averaging of multiparametric families of solutions to the Mikhal{\"e}v equation.",
keywords = "integrable system, Korteweg–de Vries equation, Mikhal{\"e}v equation, multidimensional conservation laws",
author = "Makridin, {Zakhar V.} and Pavlov, {Maxim V.}",
note = "Funding Information: ZVM and MVP are grateful to V.E. Adler, L.V. Bogdanov, E.V. Ferapontov, and S.L. Gavrilyuk for very important comments, remarks, advices, and helpful conversations. ZVM and MVP were supported by the Russian Science Foundation (grant 19‐11‐00044). Publisher Copyright: {\textcopyright} 2021 Wiley Periodicals LLC",
year = "2022",
month = feb,
doi = "10.1111/sapm.12460",
language = "English",
volume = "148",
pages = "813--824",
journal = "Studies in Applied Mathematics",
issn = "0022-2526",
publisher = "Wiley-Blackwell",
number = "2",

}

RIS

TY - JOUR

T1 - Multidimensional conservation laws and integrable systems II

AU - Makridin, Zakhar V.

AU - Pavlov, Maxim V.

N1 - Funding Information: ZVM and MVP are grateful to V.E. Adler, L.V. Bogdanov, E.V. Ferapontov, and S.L. Gavrilyuk for very important comments, remarks, advices, and helpful conversations. ZVM and MVP were supported by the Russian Science Foundation (grant 19‐11‐00044). Publisher Copyright: © 2021 Wiley Periodicals LLC

PY - 2022/2

Y1 - 2022/2

N2 - In this paper we continue investigation of a new property of two-dimensional integrable systems—existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Multicomponent two-dimensional hydrodynamic reductions of the Mikhalëv equation are considered. Infinitely many three-dimensional local conservation laws for the Korteweg–de Vries pair of commuting flows are constructed. Thus, we show that pairs of commuting dispersive two-dimensional systems also possess infinitely many local three-dimensional conservation laws. They can be used for averaging of multiparametric families of solutions to the Mikhalëv equation.

AB - In this paper we continue investigation of a new property of two-dimensional integrable systems—existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Multicomponent two-dimensional hydrodynamic reductions of the Mikhalëv equation are considered. Infinitely many three-dimensional local conservation laws for the Korteweg–de Vries pair of commuting flows are constructed. Thus, we show that pairs of commuting dispersive two-dimensional systems also possess infinitely many local three-dimensional conservation laws. They can be used for averaging of multiparametric families of solutions to the Mikhalëv equation.

KW - integrable system

KW - Korteweg–de Vries equation

KW - Mikhalëv equation

KW - multidimensional conservation laws

UR - http://www.scopus.com/inward/record.url?scp=85116888770&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4027a4b8-bcbc-3290-ae78-84e3a275442e/

U2 - 10.1111/sapm.12460

DO - 10.1111/sapm.12460

M3 - Article

AN - SCOPUS:85116888770

VL - 148

SP - 813

EP - 824

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 2

ER -

ID: 34422629