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://dx.doi.org/10.1016/j.nonrwa.2018.09.005.
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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
Original 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
WWW Nonlinear Analysis: Real World Applications
RIV identification code RIV/47813059:19610/19:A0000049
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1016/j.nonrwa.2018.09.005
UT WoS 000458714100004
Keywords in English Chains of pre-stressed granules; Compactons; Integrable systems; Conservation laws; Stability test; Numerical simulation
Tags MÚ
Tags International impact, Reviewed
Links GBP201/12/G028, research and development project.
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 28/4/2020 20:34.
Abstract
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.
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