Exact solutions to the (3+1)-dimensional coupled Klein–Gordon–Zakharov equation using exp(−Φ(ξ))-expansion method

In this article, the exp(-Φ(ξ))exp(-Φ(ξ))-expansion method is modified for (3+1)-dimensional space–time coordinate system and successfully implemented to construct the new exact traveling wave solutions of the (3+1)-dimensional coupled Klein–Gordon–Zakharov equation. The solutions of this equation are expressed in terms of hyperbolic, trigonometric, exponential and rational functions. The results illustrate its effectiveness for solving nonlinear coupled partial differential equations arises in mathematical physics and engineering. The annihilation phenomena of the wave propagation in the xx–yy plane are also investigated. Furthermore, the three-dimensional surface plots due to the obtained solutions are also given to make the dynamics of the equation visible