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
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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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
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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
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