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In this work, the closed-form analytical solutions have been generated for the complex coupled Higgs field equation through newly two efficient techniques, namely the auxiliary equation method and the extended Sinh-Gordon expansion approach. The equation under consideration introduces a quantum field, often referred to as the Higgs field, to elucidate the mechanism responsible for generating mass in gauge bosons. The approaches used achieve an extensive variety of solutions, including rational functions, hyperbolic functions, exponential functions, trigonometric functions, and Jacobian elliptical functions. Moreover, to understand the properties of the attained solutions, combined 3D-graphics and contour plots are demonstrated for specified parametric values. In particular, it has been extensively discussed that wave position and category changes with respect to different parameters for some solutions. Various attractive soliton-like solutions have been extracted, such as bell-shaped, travelling waves, periodic solitary waves, singular kink-shaped solitons, and many others. All derived solutions are substituted into the original model to ensure their accuracy. The derived solitons can be employed to investigate numerous complex phenomena associated with this model. Soliton-like solutions and travelling waves are incredible phenomena seen in a variety of domains of physics, including nonlinear waves, nonlinear optics, nonlinear dynamics, quantum physics, dusty plasma physics, engineering physics, and other nonlinear sciences fields. |
