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

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

RIV identification code

RIV/47813059:19610/19:A0000049

Organization unit

Mathematical Institute in Opava

UT WoS

000458714100004

Keywords in English

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

Tags

Tags

International impact, Reviewed

Links

GBP201/12/G028, research and development project.
Změněno: 28/4/2020 20:34, Mgr. Aleš Ryšavý

Abstract

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.