Solitary waves in modified one-dimensional Heisenberg ferromagnetic chain with linear magnetic field

Using the modified Heisenberg model，the solitary wave solutions in 1D isotropic ferromagnetic chain with linear magnetic field have been derived. It is shown that due to high-order terms in the Holstein-Primakoff spin operator transformation（i.e. terms of order ， and ，where is the spin ）we can have a solitary wave solution even in an isotropic ferromagnetic chain. At the same time linear term of magnetic field has changes the motional mode from uniformly motion to uniformly variable motion. And we found that when tend to zero, the equation can return to the case of anisotropic ferromagnetic chain.