Multi-soliton dynamics in a (3+1)-dimensional Heisenberg spin model with exchange and Dzyaloshinskii–Moriya interactions in nanowires

We present a systematic derivation and theoretical analysis of a generalized (3+1)-dimensional Kadomtsev–Petviashvili-type model governing spin-wave propagation in anisotropic ferromagnetic media with mixed transverse dispersion and coupling effects. The dynamics described by the discrete Heisenberg spin Hamiltonian are reduced to a single effective nonlinear evolution equation through the continuum Landau–Lifshitz framework and a multi-scale expansion. The use of the Bell polynomial formalism allows the model to be transformed into a bilinear form, which then facilitates the construction of explicit multi-soliton solutions. The resulting wave structures propagate robustly and collide elastically, highlighting the influence of chiral magnetic interactions on the underlying dynamic processes. Furthermore, Fourier pseudo-spectral analysis shows that these solitonic structures remain stable during propagation through ferromagnetic nanowires. This study provides insight into nonlinear excitations and localized waves in ferromagnetic nanowires.