A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients $D_A$ and $D_B$ is studied using a master equation approach in dilute and concentrated solutions. Species A and B are supposed to be engaged in the autocatalytic reaction A+B $\to$ 2A. Contrary to the results of a deterministic description, the front speed deduced from the master equation in the dilute case sensitively depends on the diffusion coefficient of species B. A linear analysis of the deterministic equations with a cutoff in the reactive term cannot explain the decrease of the front speed observed for $D_B>D_A$. In the case of a concentrated solution, the transition rates associated with cross-diffusion are derived from the corresponding diffusion fluxes. The properties of the wave front obtained in the dilute case remain valid but are mitigated by cross-diffusion which reduces the impact of different diffusion coefficients.

Fisher和Kolmogorov，Petrovskii和Piskunov类型的波前涉及具有不同扩散系数的两个物种A和B $d_{\mathrm{一种}}$ 和 $d_{乙}$使用母方程法研究稀溶液和浓溶液。物种A和B应该参与自催化反应A + B$\to$2A。与确定性描述的结果相反，在稀疏情况下从主方程推导出的前沿速度敏感地取决于物质B的扩散系数。对具有反应性项截止值的确定性方程进行线性分析无法解释观察到的前速度$d_{乙}>d_{\mathrm{一种}}$。在浓溶液的情况下，与交叉扩散有关的转变速率是从相应的扩散通量得出的。在稀化情况下获得的波前特性仍然有效，但由于交叉扩散而减弱，从而减小了不同扩散系数的影响。