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

Kód výsledku v IS VaVaI

RIV/47813059:19610/13:#0000369 - isvavai.cz

Výsledek na webu

http://iopscience.iop.org/0951-7715/26/3/757/

DOI - Digital Object Identifier

10.1088/0951-7715/26/3/757

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

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

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

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

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Nonlinearity

ISSN

0951-7715

e-ISSN

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Svazek periodika

26

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

6

Strana od-do

757-762

Kód UT WoS článku

000314825700008

EID výsledku v databázi Scopus

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