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Why nonlocal recursion operators produce local symmetries: new results and applications

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F05%3A%230000042" target="_blank" >RIV/47813059:19610/05:#0000042 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Why nonlocal recursion operators produce local symmetries: new results and applications

  • Original language description

    It is well known that integrable hierarchies in (1+1) dimensions are local while the recursion operators that generate these hierarchies usually contain nonlocal terms. We resolve this apparent discrepancy by providing simple and universal sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions to generate a hierarchy of local symmetries. These conditions are satisfied by virtually all recursion operators known today and are much easier to verify than those found in earlier work. We also give explicit formulae for the nonlocal parts of higher recursion, Hamiltonian and symplectic operators of integrable systems in (1+1) dimensions. Using these two results we prove, under some natural assumptions, the Maltsev?Novikov conjecture stating that higher Hamiltonian, symplectic and recursion operators of integrable systems in (1+1) dimensions are weakly nonlocal, i.e., the coefficients of these operators are local and these operators contain at most one integration operat

  • Czech name

    Proč nelokální operátory rekurze generují lokální symetrie: nové výsledky a aplikace

  • Czech description

    Byly nalezeny nové postačující podmínky lokality symetrií generovaných pomocí hereditárních operátorů rekurze v dimenzi (1+1). Na rozdíl od známých výsledků Sanderse a Wangové se nevyžaduje např. existence škálovací symetrie. Nalezené podmínky lokality byly využity k důkazu Malcevovy-Novikovovy domněnky o struktuře nelokálních členů vyšších operátorů rekurze, Hamiltonových a symplektických struktur v dimenzi (1+1).

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GA201%2F04%2F0538" target="_blank" >GA201/04/0538: Geometry of integrable systems</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2005

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Physics A: Mathematical and General

  • ISSN

    ISSN0305-4470

  • e-ISSN

  • Volume of the periodical

    38

  • Issue of the periodical within the volume

    15

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    11

  • Pages from-to

    3397-3407

  • UT code for WoS article

  • EID of the result in the Scopus database