The periodic wave solutions for a (2Â +Â 1)-dimensional AKNS equation

In this paper, a (2 + 1)-dimensional AKNS equation is considered. Bilinear Bäcklund transformation is presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented, and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.