This paper deals with constructing more general
exact solutions of the coupled Higgs equation by using
the (G0/G, 1/G)-expansion and (1/G0)-expansion methods.
The obtained solutions are expressed by three types
of functions: hyperbolic, trigonometric and rational functions
with free parameters. It has been shown that the suggested
methods are productive and will be used to solve
nonlinear partial differential equations in applied mathematics
and engineering. Throughout the paper, all the calculations
are made with the aid of the Maple software.