Dynamical analysis of multi-soliton and breather solutions on constant and periodic backgrounds for the (2+1)-dimensional Heisenberg ferromagnet equation

This paper focuses on a class of (2 + 1)-dimensional Heisenberg ferromagnet equation, which is an important model for describing the magnetic dynamics of ferromagnetic materials in statistical physics. Firstly, the iterative N-fold Darboux transformation is constructed and established for this (2 + 1)-dimensional equation from its known Lax pair. Secondly, starting from the trigonometric function periodic seed solutions, we not only give multi-soliton and breather solutions on three types of constant backgrounds, but also give two types of breather solutions with different parameters on the trigonometric function periodic backgrounds by using the obtained Darboux transformation. Meanwhile, the elastic interaction of the two-soliton solutions is analyzed via the asymptotic analysis technique, and the abundant structures and propagation characteristics of such soliton solutions are presented graphically. Especially, some novel soliton and breather solutions with pulse like perturbation structures propagating along the peaks and valleys on constant and periodic backgrounds are derived, under the influence of pulse perturbation propagation, some structures undergo inversion relative to the background, some structures degenerate into localized lump soliton structures, which are different from the usual soliton and breather structures on constant backgrounds. Finally, some soliton surface structures are constructed and discussed graphically. These results might have potential applications in describing magnetization motion and explaining the magnetic dynamics of ferromagnetic materials.