Traveling wave solutions of density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method

Averaging principle for multiscale stochastic reaction‐diffusion‐advection equations

“…Mathematical models of a number of physical, chemical, and biological systems are described by the reaction‐diffusion‐advection equations. The general form of reaction‐diffusion‐advection equations in one‐dimensional spatial variable is (∗) can be used to describe the dynamics of the ecological models, genetic models, gas dynamics, population distribution, etc. The chemotactic and population pressure models with bistable reaction kinetics are considered for the wave speed analysis through perturbation and Melnikov function .…”

“…( * ) can be used to describe the dynamics of the ecological models, 1,2 genetic models, 3 gas dynamics, population distribution, 4 etc. The chemotactic and population pressure models with bistable reaction kinetics are considered for the wave speed analysis through perturbation and Melnikov function.…”