Topological Gap Solitons In Bosonic Dimer Chains

In the experiment,the non-trivial topological boundary states in the one-dimensional optical lattice are observed,attracting more and more people to participate in the research on the topological properties of one-dimensional periodic optical lattice.In the mean field theory,the interaction between bosons in the periodic Bose system leads to significant nonlinear phenomena,resulting in bandgap solitons.With the deepening of the study,we can see that the boundary state and the topology in different systems and even different models,the bandgap soliton will likely show different properties,including the nonlinear Bloch boundary and topological properties,the gap The combination of soliton and nonlinear Bloch wave and the stability of boundary soliton.This paper has chosen the model as the research basis.By selecting different boundary parameters,we find that the different values of the boundary determine whether there is a boundary state in the system under the SSH model,and the energy level splitting image in the corresponding boundary state is analyzed.On the other hand,And the influence of the linear and nonlinear conditions on the distribution of the particle distribution state of the boundary state in the one-dimensional superlattice system and its wave function.In the process of research,this paper adopts the nonlinear Schrodinger equation of onedimensional bi-periodic potential to carry out numerical simulation.The difference method is used to derive its matrix form.Under the open boundary condition,the wave function of the gap soliton is discussed.Its band nature.We find that for the absence of interaction between particles,the gap soliton on the boundary can be regarded as a similarity state with a special boundary state of the topology.By analyzing the energy band,wave function and energy spectrum of the particle,The Difference and Cause of Formation of Boundary and Continuity.Finally,we discuss the bandgap soliton in the nonlinear system when the interaction of particles exists,and analyze the influence of the interaction factor on the eigenvalue of the particle,and give a brief summary.