Nonlinear evolution of Yukawa couplings in the double Higgs and supersymmetric extensions of the standard model

The nonlinear evolution equations for Yukawa coupling matrices are discussed in the context of standard, double Higgs and supersymmetric model of electroweak interactions. In each case, even the presence of a very heavy top quark the approximate analytical solutions for the nonlinear evolution of masses and mixing angles are found. Comparison of the analytical approach with numerical solutions confirm the excellent validity of the approximation. Some possible further applications of the developed method are suggested. (orig.)