Self-similar dynamics of bacterial chemotaxis
We investigate the pattern formation of colony generated by chemotactic bacteria through a continuum model. In a simplified case, the dynamics of system is governed by a density-dependent convection-reaction-diffusion equation, $u_t = (u^m)_xx - 2κ(u^m)_x+ u - u^m$. This equation admits the analytical solutions that show the self-similarity of the bacterial colony's morphogenesis. In addition, we found that the colony evolves long time as the sharp traveling wave. The roles of chemotaxis on the regulation of pattern formation in these results are also discussed.