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A complete list of conservation laws for non-integrable compacton equations of K(m,m) type

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F13%3A%230000369" target="_blank" >RIV/47813059:19610/13:#0000369 - isvavai.cz</a>

  • Result on the web

    <a href="http://iopscience.iop.org/0951-7715/26/3/757/" target="_blank" >http://iopscience.iop.org/0951-7715/26/3/757/</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1088/0951-7715/26/3/757" target="_blank" >10.1088/0951-7715/26/3/757</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A complete list of conservation laws for non-integrable compacton equations of K(m,m) type

  • Original language description

    In 1993, P Rosenau and J M Hyman introduced and studied Korteweg-de-Vries-like equations with nonlinear dispersion admitting compacton solutions, u(t) + D-x(3)(u(n))+D-x(u(m)) = 0, m, n > 1, which are knownas theK(m, n) equations. In this paper we consider a slightly generalized version of theK(m, n) equations for m = n, namely, u(t) = aD(x)(3) (u(m)) + bD(x)(u(m)), where m, a, b are arbitrary real numbers. We describe all generalized symmetries and conservation laws thereof for m not equal -2,-1/2, 0,1; for these four exceptional values of m the equation in question is either completely integrable (m = -2,-1/2) or linear (m = 0, 1). It turns out that for m not equal -2,-1/2, 0, 1 there are only three symmetries corresponding to x- and t-translationsand scaling of t and u, and four non-trivial conservation laws, one of which expresses the conservation of energy, and the other three are associated with the Casimir functionals of the Hamiltonian operator D = aD(x)(3) + bD(x) admitted b

  • Czech name

  • Czech description

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

  • Continuities

    S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2013

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Nonlinearity

  • ISSN

    0951-7715

  • e-ISSN

  • Volume of the periodical

    26

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    6

  • Pages from-to

    757-762

  • UT code for WoS article

    000314825700008

  • EID of the result in the Scopus database