2023/05/16 by Muhammad Al-Zafar Khan, Khan, Muhammad Al-Zafar, Mervlyn Moodley +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2305.09338
openalex publication_date 2023/05/16 · openalex created_date 2023/05/18 · openalex updated_date 2026/07/28
We calculate soliton solutions to the scalar field equation of motion that arises for the 4th-order extended Lagrangian (\(ϕ4\) theory) in quantum field theory using the extended hyperbolic tangent and the sine-cosine methods. Using the former technique, ten complex soliton waves are obtained; we graphically represent three of these profiles using density plots. In the latter case, two real soliton solutions are obtained, of which, we demonstrate the wave profile for the positive case. Using the multiplier method, we calculate conservation laws in \((1 + 1)\)-, \((2 + 1)\)-, and \((3 + 1)\)-dimensions producing three, six, and ten conservation laws respectively. Lastly, we reflect on the application of conservation laws in particle physics and phenomenology.