On the nonlinear Meissner equation

Abstract

The nonlinear Meissner equation is considered. The splitting of separatrices is studied via Poincaré – Mel’nikov method. The possible limits of applicability of this method due to the existence conditions of an unstable periodic solution are discussed. Nonlinear dynamics is studied numerically via Poincaré maps for certain values of the parameter. Areas of regular and chaotic behavior are revealed. Using the proposed method, periodic solutions located inside the presumable undestroyed tori are found numerically.