Vsevolod A. Vladimirov, Ekaterina V. Kutafina, Anna Pudelko, “Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology”, SIGMA, 2006, Volume 2,061, 15 pp.

This article is cited in 4 papers

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

Vsevolod A. Vladimirov, Ekaterina V. Kutafina, Anna Pudelko

Faculty of Applied Mathematics AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków Poland

Abstract: 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.

Keywords: generalized Burgers equation; telegraph equation; model of somitogenesis; direct algebraic balance method; periodic and solution-like travelling wave solutions; approximation of the soliton-like solutions.

MSC: 35C99; 34C60; 74J35

Received: November 30, 2005; in final form May 24, 2006; Published online June 19, 2006

Language: English

DOI: 10.3842/SIGMA.2006.061