Minimal velocity of the traveling wave solutions in two coupled Fisher-Kolmogorov-Petrovsky-Piskunov equations with the global conservation law

We investigate a system of two coupled one-dimensional Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equations which possess a global conservation law. Such a system of equations has been recently derived for the quasiparticle densities in a two-band fermionic model with a particle-number conserving dissipative protocol. As the standard FKPP equation, the studied system has one unstable and one stable homogeneous solution, with a traveling wave switching between them. We demonstrate that the conservation law enforces the synchronization of traveling waves for both densities and determines their minimal possible velocity. Surprisingly, we find the existence of jumps in the minimal velocity as a function of control parameters. We obtain that the minimal velocity of propagating fronts in the coupled FKPP equations may significantly exceed the minimal velocity for a single FKPP equation in a wide range of control parameters.