Traveling waves for a Lotka–Volterra competition system with diffusion

The paper addresses the existence of traveling waves for a two species competitive Lotka–Volterra reaction–diffusion system with discrete delays { ∂ ∂ t u 1 ( x , t ) = d 1 ∂ 2 ∂ x 2 u 1 ( x , t ) + r 1 u 1 ( x , t ) [ 1 − a 1 u 1 ( x , t ) − b 1 u 1 ( x , t − τ 1 ) − c 1 u 2 ( x , t − τ 2 ) ] , ∂ ∂ t u 2 ( x , t ) = d 2 ∂ 2 ∂ x 2 u 2 ( x , t ) + r 2 u 2 ( x , t ) [ 1 − a 2 u 2 ( x , t ) − b 2 u 2 ( x , t − τ 3 ) − c 2 u 1 ( x , t − τ 4 ) ] . Our results can extend some existing ones for two species diffusion competition Lotka–Volterra systems.