Different Types of Solitary Wave Scattering in the Fermi--Pasta--Ulam Model

We show that the scattering between two solitary waves in the Fermi--Pasta--Ulam model with interaction potential V(x)=αx²/2+x⁴/4 can be classified into four types according to the configurations of the solitary waves. For three of the four types, the large solitary wave can lose energy and the small one can gain in average by collision. For the other one type in a special parameter region we encounter an anomalous scattering, i.e. the large solitary wave gains energy and the small one loses energy. Numerical investigations are performed for the anharmonic limit case of α=0 and the general case of α≠0 and comparisons between them are made.