Analyzing sensitivity and modulation instability with solitary wave solutions of coupled Higgs equation describing nucleons–mesons interaction

This study examines the behavior of the coupled Higgs equation, a nonlinear model in particle physics that provides a suitable foundation for understanding electroweak symmetry breaking. We derive solitary wave (SW) solutions of the proposed model using the improved F-expansion and the Kumar–Malik methods, encompassing singular, dark, bright, periodic, M-shaped periodic, and W-shaped periodic forms. To explore their physical properties more comprehensively, we visualize selected solutions as 3D surfaces and 2D curve plots by assigning specific parameter values. Subsequently, utilizing its SW solution, we obtain the necessary condition under which our model is stable. We analyze the model’s modulation instability using linear stability theory and sensitivity by employing the Galilean transformation, and present the results graphically. Our study reveals the properties of the Higgs boson, uncovers facts about the Higgs mechanism, and promotes inquiry beyond the conventional models, unveiling the underlying dynamics of the cosmos.