On the modified versions of G′G-expansion technique for analyzing the fractional coupled Higgs system

Abstract

In this research, two modified forms of the Ḡ≡G′G-expansion method are employed to investigate various kinds of solitary wave solutions that include kink, lump, periodic, and rogue wave solutions within the framework of the fractional coupled Higgs system. The underlying patterns in the targeted model are revealed by using extended and generalized Ḡ-expansion methods. The first step involves converting the model into nonlinear ordinary differential equations via a fractional complex transformation. Following that, the suggested improved versions of the Ḡ-expansion approach are used to provide numerous solitary wave solutions. Some solitary wave solutions are represented by two- and three-dimensional graphs, demonstrating their typical propagating behavior. This research finishes by summarizing the vast findings and exploring their implications for high-energy physics.