The Speed of Traveling Waves in a FKPP-Burgers System

We consider a coupled reaction–advection–diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as one-dimensional version of model for reacting fluid in which arising density differences induce buoyancy force advecting fluid. study front propagation this through lens traveling waves solutions. are able to show two quite different behaviors depending whether coupling constant $$\rho $$ is large or small. First, it proved that there threshold _0$$ under advection has no effect speed (although nonzero). Second, when large, wave speeds must be at least $$\mathcal {O}(\rho ^{1/3})$$ . results together give transition from pulled pushed increases. Because complex dynamics involved similar models, one first precise literature solution. use mix ordinary partial differential equation methods our analytical treatment, we supplement with numerical treatment featuring newly created understand behavior speeds. Finally, various conjectures open problems formulated.