https://doi.org/10.1140/epjb/e2009-00370-5
Wavy fronts in reaction-diffusion systems with cross advection
1
Computing Centre of the Russian Academy of Sciences, Vavilova 40, 119333 Moscow, Russia
2
Institut für Theoretische Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg, Germany
3
Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya 3, 142290 Pushchino, Moscow region, Russia
4
Institut für Experimentelle Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg, Germany
Corresponding authors: a zemskov@ccas.ru e-zemskov@yandex.ru - b klaus.kassner@ovgu.de - c tsyganov@iteb.ru - d marcus.hauser@ovgu.de
Received:
2
June
2009
Revised:
30
September
2009
Published online:
31
October
2009
Bistable reaction-diffusion systems of activator-inhibitor type with cross advection are studied analytically and numerically using a piecewise linear approximation for the nonlinear reaction term. It is shown that a system with double symmetric cross advection produces the same characteristic equation as a system with cross diffusion in only one equation or a system exhibiting double self advection with opposite signs. For systems with cross-advection terms having opposite signs, traveling-wave solutions are derived explicitly. Fronts constructed from these solutions have characteristic wavy profiles. A bifurcation of excitation fronts induced by cross advection is discovered. Including cross diffusion, we find front solutions having both an oscillatory leading edge and an oscillating tail.
PACS: 82.40.Ck – Pattern formation in reactions with diffusion, flow and heat transfer / 47.20.Ky – Nonlinearity, bifurcation, and symmetry breaking / 87.23.Cc – Population dynamcics and ecological pattern formation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009
