Multi-soliton and double Wronskian solutions of a (2+12+1)-dimensional modified Heisenberg ferromagnetic system

A (2+12+1)-dimensional modified Heisenberg ferromagnetic system, which arises in the motion of magnetization vector of the isotropic ferromagnet and biological pattern formation, is investigated. Via the Hirota bilinear method, multi-soliton solutions of such a system are derived. It is proved that the system possesses the N-soliton solutions expressed in terms of the double Wronskian determinant. Head-on and overtaking elastic interactions are exhibited. Elastic interaction behavior between the two solitons has been interpreted through the asymptotic analysis, namely, amplitude and velocity of each soliton remain unchanged except for the phase shift after the interaction. Inelastic interactions including the soliton fusion and fission between two solitons are shown. During the soliton propagation, for the product of two fields, the soliton with the smaller amplitude can travel faster than with the larger, while for the third field, the soliton with the larger amplitude can travel faster than with the smaller. On the other hand, the soliton for the third field may exhibit the solitoff-like property. With respect to the three solitons, head-on elastic interaction can be found.