Lie’s Infinitesimal Continuous Parameter Similarity Transformation Method of Solving Coupled Nonlinear Partial Differential Equations and Exact Solutions of SU (2) Yang-Mills Field Equations

Abstract

Using Lie’s Infinitesimal continuous parameter similarity transformation method of solving nonlinear coupled partial differential equations is used to find two new exact solutions of Wu-Yang-t’ Hooft-Julia-Zee ansatz reduced SU(2) Yang-Mills-Higgs field equations at Prasad-Sommerfield limits. These new solutions are with trigonometric circular functions unlike known hyperbolic functions. A general method of solving coupled nonlinear partial differential equations by reducing the number of independent variables by one, this method is explained.