Theoretical Investigation Of Nonlinear Localized Wave Excitation In The Ferromagnet Spin Chain With Twist Interaction

Nonlinear excitations have attracted considerable attention in the magnetic system.In particular,the nonlinear excitation of spin waves,magnetic solitons and magnetic domain walls has become a hot issue in theoretical and experimental studies.At present,it has been confirmed that the magnetic solitons exhibit a pattern of spin motion as a collective excitation in the ferromagnetic spin chain.Furthermore,the characteristics of the magnetic moment distributions allow us to extract important information about the anisotropy and magnetization mechanisms of the samples.This makes magnetic storage,logic devices and other technology applications to be developed.On the other hand,With the continuous discovery of the research,the types of nonlinear waves are becoming more and more rich,such as solitons,breathers,rogue waves and their nonlinear superposition state,which are present in nonlinear optics,Bose-Einstein condensate and other physical systems.Therefore,we expect to find more and more kinds of nonlinear localized waves excitation in the spin chain with different interactions.In this paper,we investigated the properties and evolution of nonlinear localized waves excitation in the Heisenberg ferromagnetic spin chain with twist interaction,which includes the anti-dark soliton,W-shaped soliton,multi-peak soliton,Akhmediev breather,Kuznetsov-Ma breather and rogue wave.The magnetic moment distribution corresponding to them is characterized in detail.First,to investigate the evolution of nonlinear localized wave in spin chain with twist interactions,we construct a fourth-order integrable nonlinear Schr ¨odinger equation.By means of Darboux transformation,then,we obtained a generalized solution which contains many different types of nonlinear localized waves.According to this analytical solution,we confirmed the nonlinear excitation of solitons,breathers and rogue wave,and investigated the characteristics of magnetic moment distribution corresponds to them.The results show that the spin magnetic moment of the circular distribution near the pole of Bloch sphere represents the spin wave background.Moreover,we gave the correspondence phase diagrams between several nonlinear waves excitation and modulation instability,and based on the physical parameters of magnon number number N,perturbation wave number K,spin wave background wave number ksand amplitude c,we presented the corresponding existence conditions.These results not only enriched our understanding of nonlinear excitations in the ferromagnetic spin chain system,but also provide a theoretical basis for experimentally controlled excitation.