Abstract: Based on the experimental data and the known theories on scatters of particles, various equations (including 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