The method of sine-cosine and the method of dynamical bifurcation theory of the differentiable dynamics are employed to investigate the solitary and periodic traveling waves for the (2+1)-dimensional Maccari equation. It is shown that the (2+1)-dimensional Maccari equation gives solitary wave solution and periodic wave solution.

solitary wave solution, periodic wave solution, sine-cosine method, method of dynamical bifurcation theory of the differentiable dynamics, the (2+1)-dimensional Maccari equation.