Traveling waves solutions for a cooperative system with nonlinear advection and nonlinear KPP term

In this work, a characterization of Traveling Waves (TW) solutions to a cooperative system formulated with an order four operator, with a nonlinear advection and a Fisher-KPP reaction term is introduced. The order four operator induces a set of instabilities in the proximity of the critical points. This property can be understood from a biological perspective to describe the synchronizing effects between both species even when the diffusion is not regular. This phenomenon reflects the capability of a cooperative species system to propagate along the media while keeping cooperation even for instability regions. In addition, given a certain advection coefficient, it is possible to assess a TW-velocity for which the described instabilities do not occur. This TW-velocity has been sharply assessed. The techniques developed along this study are based on a mix of analytical and numerical approaches.