Bright and dark solitons for a variable-coefficient $$(2+1)$$ ( 2 + 1 ) dimensional Heisenberg ferromagnetic spin chain equation

Abstract

Under investigation in this paper is a variable-coefficient $$(2+1)$$ dimensional Heisenberg ferromagnetic spin chain equation. Bilinear forms for the bright and dark soliton solutions are respectively obtained. Bright and dark solitons are obtained via the Hirota bilinear method. Features of the bright and dark solitons are discussed. Interaction properties of the bright and dark solitons are discussed via the asymptotic analysis, and stability of the bright and dark solitons is studied via the numerical calculation: (1) Amplitudes of the bright and dark solitons are not related to the coefficient $$\delta _{4}(t)$$ , while the soliton velocities are related to $$\delta _{4}(t)$$ . (2) Interactions between the bright two solitons are shown to be elastic, while interactions between the dark two solitons could be elastic or inelastic, which is determined by the values of $$\rho $$ . (3) Numerical calculation indicates that the bright solitons could not resist the disturbance of small perturbations, while the dark solitons could resist the disturbance of small perturbations.