Rigorous numerical study of symmetry breaking in a pair of nonlinear cylinders

Symmetry breaking refers to the existence of solutions that break the original symmetries of the underlying nonlinear system. In nonlinear optics with Kerr nonlinearity, symmetry breaking has been studied in serval complex structures by some approximate semi-analytical methods. In this paper, we develop an efficient numerical method to rigorously analyze symmetry breaking in a simple system of two circular cylinders with Kerr nonlinearity. The rigorous numerical studies and detailed analysis can lead to better understanding and practical applications of symmetry breaking.