This review summarizes all known results (up to this date) about methods of integration of
the classical Lotka–Volterra systems with diffusion and presents a wide range of exact …

We analyze the transition between pulled and pushed fronts both analytically and
numerically from a model-independent perspective. Based on minimal conceptual …

This paper is concerned with some spreading properties of monostable Lotka–Volterra two‐
species competition‐diffusion systems when the initial values are null or exponentially …

This paper is devoted to investigating the propagation speed and direction of the bistable
traveling wave for the Lotka–Volterra competition model with bistable nonlinearity. A range …

We consider the classical two-species Lotka-Volterra competition-diffusion system in the
strong-weak competition case. When the corresponding minimal speed of the traveling …

The main purpose of this paper is to study the traveling wave solutions of the diffusive Lotka–
Volterra systems with boundary conditions. With the help of Gröbner bases elimination …

We show that propagation speeds in invasion processes modeled by reaction–diffusion
systems are determined by marginal spectral stability conditions, as predicted by the …

Existence, uniqueness and stability of forced pulsating waves as well as gap formation of
reaction diffusion models in a shifting habitat are challenging problems in the field of …

The sign of bistable wave speed indicates the propagation direction of bistable wavefronts.
This paper deals with the propagation dynamics of bistable traveling waves for abstract …

In this paper, we investigate the invading speeds for a three-species competition system. By
deriving the existence and non-existence of a class of traveling waves connecting two …