Analytical and Numerical Treatment of a Nonlinear Equation in Effective Particle Dynamics

Document Type : Research Article

Author

School of Physics, Damghan University, Damghan, 3671641167, Iran; Canadian Quantum Research Center, 106-460 Doyle Ave, Kelowna, British Columbia V1Y 0C2 Canada

Abstract

Nonlinear equations frequently arise in effective models of particle physics, particularly in the description of bound states, mass renormalization, and self-consistent field theories. In this paper we investigate a representative nonlinear integral, differential equation motivated by self-energy corrections in scalar field theory. We provide both approximate analytical solutions and numerical analysis, uncovering stability properties and physical implications for mass shifts and resonance structures. Our results indicate the existence of multiple solution branches, with physical relevance determined by energy minimization. This study highlights the subtle interplay between nonlinearities and renormalized observables in particle dynamics.

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Volume 10, Issue 1
December 2025
Pages 50-59
  • Receive Date: 10 November 2025
  • Revise Date: 07 December 2025
  • Accept Date: 15 December 2025
  • Publish Date: 17 December 2025