Solutions of the generalized Bogomol'nyi equations via monotone iterations

This paper is concerned with the numerical solutions of the classical Abelian Higgs vortex model in R² in the critical coupling phase. A globally convergent monotone iterative method will be presented to approximate finite energy multivortex solutions of both the classical and the generalized Bogomol'nyi equations. In the latter context, it is illustrated through a series of numerical examples that the Higgs potential density function may be adjusted to realize in a wide range fairly different magnetic concentration pictures of the model.