We present a theoretical investigation of the soliton dynamics of a Heisenberg ferromagnetic spin chain in the continuum limit, incorporating the combined effects of helicity and the Dzyaloshinskii–Moriya interaction (DMI). Adopting a semi-classical approach based on the Holstein–Primakoff transformation and Glauber’s coherent state representation, we derive a perturbed nonlinear Schrödinger equation (NLSE) using the multiple-scale perturbation technique. Our analysis reveals that the DMI exerts a pronounced influence on the amplitude of soliton solutions, whereas the effect of helicity on the wave profile is comparatively minimal. Notably, the velocity of the soliton remains unaffected by either interaction; however, amplitude fluctuations emerge due to their presence. Using Hirota’s bilinearization method, we construct explicit oneand two-soliton solutions and examine their collision dynamics. The results indicate that soliton interactions are inelastic in the presence of DMI, leading to suppression of the amplitude post-collision. A comparison with recent studies in the discrete regime supports the conclusion that DMI plays a dominant role in governing the intensity and stability of solitonic excitation’s in helimagnetic systems.
Sunny et al. (Thu,) studied this question.