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 and Vsevolod A. VLADIMIROV

Basic information

Original name

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

Authors

SERGYEYEV, Artur (804 Ukraine, belonging to the institution); Sergiy I. SKURATIVSKYI (804 Ukraine) and Vsevolod A. VLADIMIROV (804 Ukraine)

Edition

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

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

is not subject to a state or trade secret

References:

Nonlinear Analysis: Real World Applications

Impact factor

Impact factor: 2.072

RIV identification code

RIV/47813059:19610/19:A0000049

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1016/j.nonrwa.2018.09.005

UT WoS

000458714100004

EID Scopus

2-s2.0-85055878467

Keywords in English

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

Links

GBP201/12/G028, research and development project.

Changed: 28/4/2020 20:34, Mgr. Aleš Ryšavý

Abstract

In the original language

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.

Cite

SERGYEYEV, Artur; Sergiy I. SKURATIVSKYI and 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, vol. 47, June, p. 68-84. ISSN 1468-1218. Available from: https://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 = {https://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 and 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, vol.~47, June, p.~68-84. ISSN~1468-1218. Available from: https://doi.org/10.1016/j.nonrwa.2018.09.005.

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