Pfaffianization of the discrete three-dimensional three wave interaction equation

We first present the discrete Gram-type determinant solution to the discrete three-dimensional three wave interaction equation. Then a pfaffianized version of the discrete three-dimensional three wave interaction equation is produced by using Hirota and Ohta's pfaffianization procedure. The Gram-type pfaffian solution to the resulting system is also given. In addition, we obtain the soliton solutions of the resulting system as an example of the Gram-type pfaffian solution.