中文摘要：

基于粒子散射的实验结果和已知的理论，首先，讨论了散射的各种方程，包括Lipkin方程、Pearson方程和Laguerre方程等，并且应用于各种散射；其次，重点研究了非线性方程，如KdV方程、非线性统一方程等及其孤子解；然后，探讨了共振态和弹性、非弹性碰撞；进而，讨论高能散射和相应的统计模型；最后，提出不同能量的散射可能对应粒子低能具有对称性和高能具有统计性的新二重性。

英文摘要：

Based on the experimental data and the known theories on scatters of particles , various equations （ in-cluding the Lipkin equation , the Pearson equation and the Laguerre equation , etc.） of scatters were discussed , and these equations were applied in various scatters .Next, the nonlinear equations , for example, the KdV equation and the nonlinear unified equation , etc., and their soliton solutions were investigated importantly .Then the resonances , elastic and non-elastic collisions were researched .Further, the scatters at high energy and corresponding statistical models were discussed.Finally, it was proposed that the scatters with different energies correspond probably to the new duality of particles that possess the symmetry for low energy and the statistics for high energy .