Interactions of Parametrically Driven Dark Solitons. II: N\'eel-Bloch interactions

Abstract

The interaction between a Bloch and a N\'eel wall in the parametrically driven nonlinear Schr\"odinger equation is studied by following the dissociation of their unstable bound state. Mathematically, the analysis focusses on the splitting of a four-fold zero eigenvalue associated with a pair of infinitely separated Bloch and N\'eel walls. It is shown that a Bloch and a N\'eel wall interact as two classical particles, one with positive and the other one with negative mass.