Background: In previous papers it was set out that matter could be considered to be formed by gravitational pulsations in a hexadimensional space with anisotropic curvature, since solutions to Einstein's field equations presented all of the characteristics of a particle then. Results: Four solutions to the gravitational wave equation have been found . These solutions can be assimilated to four neutrinos and complement to the previous solution identified with the electron. Since this set of solutions does not allow the existence of hadrons is postulated the existence of a central hole in the plane of the compacted dimensions. By assuming this postulate we can obtain complementary solutions formed by a surface wave plus any of the other five solutions. These solutions are called glutinos. Linear combinations of these solutions can explain the huge variety of known particles, allowing not only to identify their different charges, but also justify the existence of a multilinear system for hadron masses as advocated by Palazzi. The proposed system also predict the size of mesons and baryons, and the internal distribution of charges. Regarding interactions, they occur via three non-linear mechanisms: by changing the refractive index, deforming and dragging on propagation medium (space-time). No other interaction is possible . The first two are the source of the gravitational interaction, the residual nuclear force and the London interaction, while the latest is the origin of interactions similar to the electromagnetic interaction. These interactions have been called electrostrong, electromagnetic and electroweak interaction. We can obtain mathematically these interactions from the probability density of the wavefunction or from the wavefunction gradient.