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New precise solitary wave solutions for coupled Higgs field equations via two enhanced methods
Usman Hassan1,2, Jamilu Sabi'u1, Usman Abbas Yakubu1
1Mathematics Department, Northwest University Kano, Kano, Nigeria.
Scientific Reports
|August 14, 2025
Summary
Researchers explored solitary wave solutions for coupled Higgs field equations using advanced mathematical methods. They discovered diverse soliton types, offering insights into nonlinear physics and potential applications in quantum physics and data science.
Area of Science:
- * Mathematical Physics
- * Nonlinear Dynamics
Background:
- * Coupled Higgs field equations model conserved scalar nucleons interacting with neutral scalar mesons.
- * Understanding solitary wave solutions is crucial for nonlinear systems.
Purpose of the Study:
- * To find precise solitary wave solutions for the coupled Higgs field equations.
- * To investigate the formation and characteristics of various soliton types.
Main Methods:
- * Employed the enhanced Sardar sub-equation and generalized Riccati equation methods.
- * Utilized a traveling wave transformation to convert the model into nonlinear ordinary differential equations.
- * Visualized solutions using Maple 18 with 2D and 3D plots.
Main Results:
- * Identified diverse soliton solutions: periodic, dark-bell, bright, and anti-bell.
- * Solutions were expressed using exponential, hyperbolic, rational, and trigonometric functions.
- * Demonstrated solution behavior by varying parameters.
Conclusions:
- * The applied methods are effective, straightforward, and do not require linearization or specific conditions.
- * Findings offer novel insights into nonlinear behaviors in physical systems.
- * Results are original and contribute to the field of nonlinear partial differential equations.
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