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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 10 scientific papers (total in 10 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 (10)
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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 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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