Dynamics of novel positons in a high-dimensional Heisenberg ferromagnet through Darboux transformation

Abstract We investigate nonlinear magnetic excitations in the ( 2 + 1 ) -dimensional Heisenberg ferromagnetic spin equation using the n -fold Darboux transformation. Exact analytical solutions, including dark, bright, and breather-type solitons, are constructed in determinant form. By employing a degenerate spectral limit, we derive higher-order smooth positon and breather–positon solutions. The determinant representation enables systematic analysis of their decomposition, interaction behavior, and phase shifts. Furthermore, trajectory analysis on the Bloch sphere provides physical insight into the precessional dynamics of localized magnetization vectors. These results reveal rich nonlinear interaction patterns arising from higher-dimensional effects in ferromagnetic media.