Excitation of nonlinear solitary flexural waves in a moving domain wall

Numerical methods have been used to study the dynamics of a 180 °C domain wall described by a modified sine-Gordon equation, in an infinite ferromagnet with a weak ferromagnetism. The dynamics of solitary flexural waves, which appear upon the intersection of a domain wall with a local region of material with magnetic-anisotropy parameters differing from those of the basic volume of the ferromagnet, has been investigated. The case where the width of the domain wall and the size that characterizes the inhomogeneity of the magnetic-anisotropy parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde K $$\end{document} are of the same order is considered. It is shown that a solitary flexural wave can be considered as one of the “kink-on-kink” solutions of the sine-Gordon equation.