Travelling wave solutions in non-local convolution diffusive competitive-cooperative systems

In this paper, we investigate the existence of travelling wave solutions for the non-local convolution diffusion two-species competitive-cooperative systems by using Schauder's fixed-point theorem and a cross-iteration technique. If the non-local diffusion kernel J(1)(x) = J(2)(x) = delta(x) + delta(n)(x) where is the Dirac delta function, then we can obtain the results in Huang & Zou (2006, Travelling wave solutions in delayed reaction diffusion systems with partial monotonicity. Acta Math. Appl. Sinica, 22, 243-256) and the existence of travelling waves for the corresponding Laplacian diffusion two-species competitive-cooperative systems.