Painlevé Analysis and Soliton Solutions for an Inhomogeneous Heisenberg Ferromagnetic System

In this paper we investigate an inhomogeneous higher-order nonlinear Schrödinger equation generated from the deformation of an inhomogeneous Heisenberg ferromagnetic system. Considering the variable coefficients from the inhomogeneities in the ferromagnetic medium, we present the Painlevé-integrable condition. Introducing an auxiliary function, we obtain the one-, two- and N-soliton solutions via the Hirota method. Furthermore, we graphically analyze the influence of inhomogeneities on the soliton propagation and interaction. It is found that the inhomogeneities will cause an increasing-decreasing process of soliton amplitude, and the change of the propagation direction. The perturbation terms can affect the propagation region of soliton but have no influence on the soliton amplitude. We consider the interactions between/among two and three solitons with the same or different initial propagation directions, and observe that the inhomogeneities can influence the soliton amplitudes and propagation directions, while the perturbation parameter can only affect the propagation direction of the soliton. In addition, bound state of solitons and its interaction with soliton are analyzed under the given excitation condition.