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Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
Інший ID:
2000 Mathematics Subject Classification: 35C99; 34C60; 74J35
Посилання:
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.
Підтримка:
The authors thank the anonymous referees for helpful suggestions concerning the presentation of results.
Дата:
2006
Переглядів:
601
Завантажень:
264
Анотація:
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.
