
SIGMA 2 (2006), 061, 15 pages mathph/0606042
https://doi.org/10.3842/SIGMA.2006.061
Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
Vsevolod A. Vladimirov, Ekaterina V. Kutafina and Anna Pudelko
Faculty of Applied Mathematics AGH University of Science and Technology,
Al. Mickiewicza 30, 30059 Kraków, Poland
Received November 30, 2005, in final form May 24, 2006; Published online June 19, 2006
Abstract
We present a review of our recent works directed towards
discovery of a periodic, kinklike and solitonlike 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.
Key words:
generalized Burgers equation; telegraph equation; model of somitogenesis; direct algebraic balance method; periodic and solutionlike travelling wave solutions; approximation of the solitonlike solutions.
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