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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 181, Number 2, Pages 276–295
DOI: https://doi.org/10.4213/tmf8722 (Mi tmf8722) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Necessary integrability conditions for evolutionary lattice equations

V. E. Adler

Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia
Full-text PDF (496 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf8722
Abstract: We study the structure of solutions of the Lax equation $D_t(G)=[F,G]$ for formal series in powers of the shift operator. We show that if an equation with a given series $F$ of degree $m$ admits a solution $G$ of degree $k$, then it also admits a solution $H$ of degree $m$ such that $H^k=G^m$. We use this property to derive necessary integrability conditions for scalar evolutionary lattices.
Keywords: Volterra-type lattice, higher symmetry, conservation law, integrability test.
Received: 01.06.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 181, Issue 2, Pages 1367–1382
DOI: https://doi.org/10.1007/s11232-014-0218-2
Bibliographic databases:
PACS: 02.30.Ik
MSC: 37K10
Language: Russian
Citation: V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, TMF, 181:2 (2014), 276–295; Theoret. and Math. Phys., 181:2 (2014), 1367–1382
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:63
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