[en] A four-body model is used in studying the four-nucleon system. This model is solvable and can be applied to nuclear reactions involving four nucleons. Intermediate quasiparticle states are used for the two- and three-body scattering leading to T matrices which are separable. The model leads to four-body equations which by using partial wave decomposition are reduced to single variable integral equations. Numerical calculations of the differential cross-sections of the nuclear reactions ²H(d,p)³H, ²H(d,n)³He and ²H(d,d)²H are carried out for different deuteron laboratory energies between 6.1 MeV and 51.5 MeV. Inclusion of the p-wave three-body amplitudes is tested. Also, the simultaneous exchange of two nucleons between the incoming deuterons is investigated. The theoretically calculated angular distributions are in good agreement with the experimental measurements. The extracted values of the spectroscopic and normalization factors are reasonable. (author)