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.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
