Compacton solutions and (non)integrability of nonlinear
evolutionary PDEs associated with a chain of prestressed
granules

J 2019

Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

SERGYEYEV, Artur, Sergiy I. SKURATIVSKYI a Vsevolod A. VLADIMIROV

Základní údaje

Originální název

Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

Autoři

SERGYEYEV, Artur (804 Ukrajina, domácí), Sergiy I. SKURATIVSKYI (804 Ukrajina) a Vsevolod A. VLADIMIROV (804 Ukrajina)

Vydání

Nonlinear Analysis: Real World Applications, Oxford, England, Elsevier Limited, 2019, 1468-1218

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Nonlinear Analysis: Real World Applications

Kód RIV

RIV/47813059:19610/19:A0000049

Organizační jednotka

Matematický ústav v Opavě

DOI

http://dx.doi.org/10.1016/j.nonrwa.2018.09.005

UT WoS

000458714100004

Klíčová slova anglicky

Chains of pre-stressed granules; Compactons; Integrable systems; Conservation laws; Stability test; Numerical simulation

Štítky

MÚ

Příznaky

Mezinárodní význam, Recenzováno

Návaznosti

GBP201/12/G028, projekt VaV.

Změněno: 28. 4. 2020 20:34, Mgr. Aleš Ryšavý

Anotace

V originále

We present the results of study of a nonlinear evolutionary PDE (more precisely, a one-parameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in question supports solitary waves of compression and rarefaction (bright and dark compactons) and can be written in Hamiltonian form. We investigate inter alia integrability properties of this PDE and its generalized symmetries and conservation laws. For the compacton solutions we perform a stability test followed by the numerical study. In particular, we simulate the temporal evolution of a single compacton, and the interactions of compacton pairs. The results of numerical simulations performed for our model are compared with the numerical evolution of corresponding Cauchy data for the discrete model of chain of pre-stressed elastic granules.

Citovat

SERGYEYEV, Artur, Sergiy I. SKURATIVSKYI a Vsevolod A. VLADIMIROV. Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules. Nonlinear Analysis: Real World Applications. Oxford, England: Elsevier Limited, 2019, roč. 47, June, s. 68-84. ISSN 1468-1218. Dostupné z: https://dx.doi.org/10.1016/j.nonrwa.2018.09.005.

@article{32822,
   author = {Sergyeyev, Artur and Skurativskyi, Sergiy I. and Vladimirov, Vsevolod A.},
   article_location = {Oxford, England},
   article_number = {June},
   doi = {http://dx.doi.org/10.1016/j.nonrwa.2018.09.005},
   keywords = {Chains of pre-stressed granules; Compactons; Integrable systems; Conservation laws; Stability test; Numerical simulation},
   language = {eng},
   issn = {1468-1218},
   journal = {Nonlinear Analysis: Real World Applications},
   title = {Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules},
   url = {https://www.sciencedirect.com/science/article/pii/S1468121818310101?via%3Dihub},
   volume = {47},
   year = {2019}
}

TY  - JOUR
ID  - 32822
AU  - Sergyeyev, Artur - Skurativskyi, Sergiy I. - Vladimirov, Vsevolod A.
PY  - 2019
TI  - Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules
JF  - Nonlinear Analysis: Real World Applications
VL  - 47
IS  - June
SP  - 68-84
EP  - 68-84
PB  - Elsevier Limited
SN  - 14681218
KW  - Chains of pre-stressed granules
KW  - Compactons
KW  - Integrable systems
KW  - Conservation laws
KW  - Stability test
KW  - Numerical simulation
UR  - https://www.sciencedirect.com/science/article/pii/S1468121818310101?via%3Dihub
L2  - https://www.sciencedirect.com/science/article/pii/S1468121818310101?via%3Dihub
N2  - We present the results of study of a nonlinear evolutionary PDE (more precisely, a one-parameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in question supports solitary waves of compression and rarefaction (bright and dark compactons) and can be written in Hamiltonian form. We investigate inter alia integrability properties of this PDE and its generalized symmetries and conservation laws. For the compacton solutions we perform a stability test followed by the numerical study. In particular, we simulate the temporal evolution of a single compacton, and the interactions of compacton pairs. The results of numerical simulations performed for our model are compared with the numerical evolution of corresponding Cauchy data for the discrete model of chain of pre-stressed elastic granules.
ER  -

SERGYEYEV, Artur, Sergiy I. SKURATIVSKYI a Vsevolod A. VLADIMIROV. Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules. \textit{Nonlinear Analysis: Real World Applications}. Oxford, England: Elsevier Limited, 2019, roč.~47, June, s.~68-84. ISSN~1468-1218. Dostupné z: https://dx.doi.org/10.1016/j.nonrwa.2018.09.005.

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