Considering the importance of using nonlinear evolution equations in the investigation of many natural phenomena, we consider the \((2+1)\) -dimensional Date–Jimbo–Kashiwara–Miwa ( \((2+1)\) -dimensional DJKM) equation. Using the multiple exp functions method, we obtain analytical solutions for this equation, which are one-soliton, two-soliton, and three-soliton solutions and these solutions include three categories of soliton wave solutions, i.e., one-wave solutions, two-wave solutions, and three wave solutions. We have performed all calculations with a computer algebra system such as Maple and have also provided a graphical representation of the obtained solutions.