  In this paper we investigate the one-dimensional parabolic-parabolic
Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion
coefficient of chemical substance is equal to two, in terms of travelling wave
variables the reduced system appears integrable and allows the analytical
solution. We obtain the exact soliton solutions, one of which is exactly the
one-soliton solution of the Korteweg-de Vries equation.
