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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2006 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146111 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862575204249632768 |
|---|---|
| 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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| first_indexed | 2025-11-26T13:21:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146111 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T13:21:33Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT vladimirovva constructingsolitonandkinksolutionsofpdemodelsintransportandbiology AT kutafinaev constructingsolitonandkinksolutionsofpdemodelsintransportandbiology AT pudelkoa constructingsolitonandkinksolutionsofpdemodelsintransportandbiology |