Solitary Wave Solutions for the Dispersive Concatenation Model with and without Delays

This paper investigates the dispersive concatenation model (DCM), both in the absence and presence of local distributed delay or nonlocal delay. First, by the dynamic system method, the phase portraits of bifurcations for the DCM are categorized into five cases. Then, various bounded solitons of the DCM without a delay are derived through integration along different orbits. Finally, by using the geometric singular perturbation theory, it is proven that the DCM with local distributed delay or nonlocal delay admits the corresponding solitary wave solutions and periodic wave solutions for a certain wave speed. The analytic representations and theoretical existence of soliton solutions are helpful for deeply understanding and research on the dynamic properties of soliton solutions.