The Properties Of Nonlinear Excitation In The One-dimensional FPU-?? Model And Its Influence On Energy Transport

We know that the essence of the world is nonlinear,the nonlinear phenomenon exists widely in nature,the first record of nonlinear wave goes back to Russell in 1834 for the first time in a observed solitary wave in the canal.With the development of science,the researchers on the study of the heat transfer process,Two nonlinear excitation modes were found,we call it a soliton and breathing,they may be in the process of heat conduction plays an important role,is this article main research on soliton,for breathing only do the simple work.For solitons,we mainly studied the symmetry of interaction between the particle effects on discrete wave mechanics properties.First of all,we constructed a one-dimensional FPU—?? lattice model.In this model,we can excite two kinds of solitary waves,which are Kink and Antikink respectively.It is well known that there are three types of collisions,namely Kink-Antikink collision,Antikink-Antikink collision and kink-kink collision.In the research process,we found that:(1)the excitation soliton has a momentum threshold,which depends on the symmetry of the interaction between the microscopic particles,and the degree of symmetry is determined by alpha.(2)With lower,Kink(Antikink)excitation threshold decrease(increase);Heterogeneous solitary wave scattering rate increases,and the same between the solitary wave scattering behavior almost unaffected.According to the nature,we put forward a new method of measuring the scattering rate,In Kink-Antikink soliton collision,and thus find that there is a strong dependence on the heat conduction in the heat conduction.Fortunately,such speculation is indeed verified by the detailed examination of the time attenuation behavior of our convective correlation function,but it only applies to the early stage.Therefore,The results may indicate that soliton in relatively short time that exist in the thermal environment,which will eventually affect transportation in a short time.Breather is widespread in the localized excitation model of nonlinear system,in one dimensional lattice system energy transport process,plays an important role.But the exact mechanism is not clear.My main goal is to understand the breathing and to get the breath through numerical simulation.In the process,I did a research on the composition of the breathing,and obtained some research results.The next step is to explore the impact of breathing on energy transport.