Traveling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system

In this article, the exp(−Φ(ξ))-expansion method has been successfully implemented to seek traveling wave solutions of the coupled Higgs field equation and the Maccari system. The result reveals that the method together with the first order ordinary differential equation is a very influential and effective tool for solving coupled nonlinear partial differential equations in mathematical physics and engineering. The obtained solutions have been articulated by the hyperbolic functions, trigonometric functions and rational functions with arbitrary constants. Numerical results together with the graphical representation explicitly reveal the high efficiency and reliability of the proposed algorithm.