Analysis of wave structures for the coupled Higgs equation modelling in the nuclear structure of an atom

The aim of this paper is to produce travelling wave solutions in different forms of the coupled Higgs equation, which was first noticed in 1964 and come to the fore with its applications every day and to examine the physical behaviour of these solutions. Modified 1 / G ′ and G ′ / G , 1 / G expansion methods have been applied in order to generate complex hyperbolic, complex trigonometric and complex rational solutions. The generated travelling wave solutions have been compared to various solutions from the literature, with the emphasis on the fact that these solutions were in a more general form. The algeneralization of the solutions to the coupled Higgs equation is provided using both expansion approaches. In addition, the physical properties of the solutions have been examined by defining the special relations between the wave number and the wave velocity in the traditional wave transformation applied in both expansion methods. The graphs that the travelling wave solutions discovered in this work depict have undergone geometric analysis and can be flattened in a single plane without undergoing distortion. The presented methods are clear and precise, they may be used to examine the travelling wave theory in physics.