Magnetic soliton and breather interactions for the higher-order Heisenberg ferromagnetic equation via the iterative N-fold Darboux transformation

Abstract

This paper focuses on a higher-order Heisenberg ferromagnetic equation, which may describe the motion of the magnetic vector of isotropic ferromagnetism. The iterative N-fold Darboux transformation is first constructed to generate the dark and anti-dark magnetic solitons on the non-zero constant backgrounds, bright and dark breathers on the trigonometric function and non-zero constant backgrounds as well as breathers on the trigonometric function and vanishing backgrounds. We discover that the soliton structures of three different components can generate rotation with different constant seed solutions. Meanwhile, the trajectory curve and the direction of the magnetic vector are also discussed from the perspective of magnetism, we find that for constant seed solutions, the motion of the magnetic vector is limited to the hemisphere, while for trigonometric seed solutions, the motion of the magnetic vector can be distributed throughout the whole sphere. These novel phenomena may be helpful to understand the dynamics of the magnetic vector in the magnetic materials.