Study On The Structure And Stability Of Discrete Breather Based On Fully Discrete PN Equation

To a certain extent,breather can be regarded as a"dislocation coupler"caused by periodic oscillation caused by the interaction between two positive and negative dislocations.Dislocations are closely related to the arrangement of atoms in crystals,which can affect the brittle-plastic properties of materials microscopically,so the study of dislocation defects is of great significance.The discrete breather exists in various discrete models,and the experimental observation also proves the existence of the discrete breather,so the study of the discrete breather is a hot direction.Through the literature investigation,it is found that there is no related report on the research of discrete breather based on PN model.Finding the discrete breather based on PN theory is the biggest highlight of this paper.After finding the discrete breather,the effects of parameters ω_s and β on the discrete breather structure are discussed.The results show that ω_s has an obvious effect on the discrete respiratory substructure,and the range in which discrete inhalers can exist is 0.85<ω_s<1.15.Moreover,with the increase ofω_s,the locality of the space will decrease,specifically,the structure changes from"thin and tall"to"short and fat",but there is no structural phase transition in the middle.At the same time,the period T decreases linearly with the increase of ω_s.When the force constant β<0.6,the discrete respiratory substructure can exist.When β<0.4,the discrete breather can exist stably.When β=0.6,the stability of the discrete respiratory substructure decreases obviously,and there is an obvious diffusion phenomenon.When β<0.4,there is an obvious linear relationship between the force constantβand the time T period,and the period decreases linearly with the increase ofβ.Moreover,the influence of ω_son the period reduction is greater than that of β on the period T,indicating that the effect of ω_son the discrete breather is dominant.