The Burgers equation can describe some phenomena such as turbulence, shock wave and traffic flow dynamics problems. Under consideration in this paper is a discrete Burgers equation, which can be viewed as the discrete counterpart of Burgers equation. Firstly, we correspond this discrete equation...

In this paper, the position controllable discrete analytical higher-order rogue wave and periodic wave solutions in the semi-discrete complex coupled dispersionless system, as well as their mixed interaction phenomena, are theoretically provided in this study. Our first priority is to study the...