Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology

We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of t...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2006
Автори: Vladimirov, V.A., Kutafina, E.V., Pudelko, A.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2006
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/146111
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology / V.A. Vladimirov, E.V. Kutafina, A. Pudelko // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 19 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Vladimirov, V.A.
Kutafina, E.V.
Pudelko, A.
author_facet Vladimirov, V.A.
Kutafina, E.V.
Pudelko, A.
citation_txt Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology / V.A. Vladimirov, E.V. Kutafina, A. Pudelko // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 19 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of the direct algebraic balance method. In the case when the analytical description fails, we propose to approximate invariant travelling wave solutions by means of an infinite series of exponential functions. The effectiveness of the method of approximation is demonstrated on a hyperbolic modification of Burgers equation.
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spelling Vladimirov, V.A.
Kutafina, E.V.
Pudelko, A.
2019-02-07T13:39:10Z
2019-02-07T13:39:10Z
2006
Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology / V.A. Vladimirov, E.V. Kutafina, A. Pudelko // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 19 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 35C99; 34C60; 74J35
https://nasplib.isofts.kiev.ua/handle/123456789/146111
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of the direct algebraic balance method. In the case when the analytical description fails, we propose to approximate invariant travelling wave solutions by means of an infinite series of exponential functions. The effectiveness of the method of approximation is demonstrated on a hyperbolic modification of Burgers equation.
The authors thank the anonymous referees for helpful suggestions concerning the presentation of results.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
Article
published earlier
spellingShingle Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
Vladimirov, V.A.
Kutafina, E.V.
Pudelko, A.
title Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
title_full Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
title_fullStr Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
title_full_unstemmed Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
title_short Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
title_sort constructing soliton and kink solutions of pde models in transport and biology
url https://nasplib.isofts.kiev.ua/handle/123456789/146111
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AT kutafinaev constructingsolitonandkinksolutionsofpdemodelsintransportandbiology
AT pudelkoa constructingsolitonandkinksolutionsofpdemodelsintransportandbiology