Nonlinear excitations in ferromagnetic chains with nearest- and next-nearest-neighbor exchange interactions

Weakly nonlinear excitations in one-dimensional isotropic Heisenberg ferromagnetic chains with nearest- and next-nearest-neighbor exchange interactions are considered. Based on the properties of modulational stability of corresponding linear spin waves, the existence regions of bright and dark magnetic solitons of the system are discussed in the whole Brillouin zone. The antidark soliton mode which is convex soliton superimposed with a plane wave component is obtained near the zero-dispersion points of the spin wave frequency spectrum. The analytical results are checked by numerical simulations.