We have just solved the traveling wave solution for explicit-time nonlinear photorefractive dynamics equation. Nonlinearity comes from the support of linear and quadratic electro-optic effects. We investigated two cases, the wave was assumed to be in low amplitude and without such an assumption. In this step, we apply the direct solution method by setting the ansatz of the wave solution from the start. In the first case, the Taylor series expansion is relied on, the equations of these results can be integrated, and we get an exact solution for the traveling wave. In the second case, the original dynamic equation is fully evaluated. They are reduced to a first-order differential equation which we have provided the initial conditions for a numerical evaluation. The exact solution shows the propagation wave traveling in the positive and negative directions in the diffraction axis direction. There is also an angle between the traveling wave and the center of the propagation plane, which decreases as the value of the displacement constant in the solution increases. While the power of the traveling wave, it is also unique. Lastly, the numerical solution gives a kink-like traveling wave.