Soliton–antisoliton interaction in a parametrically driven easy-plane magnetic wire

• We study the interactions of solitons with opposite polarity with the LLG equation.
• We found that there exists both annihilative and repulsive interactions.
• Similar results we found for the Parametrically Driven and Damped NLS equation.
• We obtain an approximate analytical solution for the repulsive interaction.

In the present work we study the soliton–antisoliton interaction in an anisotropic easy-plane magnetic wire forced by a transverse uniform and oscillatory magnetic field. This system is described in the continuous framework by the Landau–Lifshitz–Gilbert equation. We find numerically that the spatio-temporal magnetization field exhibits both annihilative and repulsive soliton–antisoliton interactions. We also describe this system with the aim of the associated Parametrically Driven and Damped Nonlinear Schrödinger amplitude equation and give an approximate analytical solution that roughly describes the repulsive interaction.