Collision of perturbed soliton in discrete ferromagnetic spin chain with nearest neighbor and next nearest neighbor Dzyaloshinskii-Moriya interaction

We study the effect of next nearest neighbor Dzyaloshinskii-Moriya (DM) interaction on collision of perturbed solitons in a discrete ferromagnetic spin chain. This system includes nearest neighbor and next nearest neighbor DM interaction. We consider the Heisenberg Hamiltonian model of ferromagnetic spin chain, which takes into account both nearest neighbor and next nearest neighbor DM interaction. Using the quasi-classical approximation, we transform the Hamiltonian into the discrete nonlinear Schro<spacing diaeresis>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{o}$$\end{document}dinger (DNLS) equation. The DNLS equation describes the complete dynamics of the ferromagnetic spin chain. The discrete Hirota bilinearization method is employed to construct the one-soliton and two-soliton solutions of the DNLS equation. The two-soliton solutions are utilized to discuss the impact of nearest neighbor and next nearest neighbor DM interactions on the collision of solitons in the ferromagnetic spin chain. Additionally, we delve into the phase shift and intensity redistribution during the collision of solitons in a ferromagnetic spin chain.