Minimal velocity of the travelling wave solutions in two coupled FKPP equations with the global conservation law

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