Nonlinear Gravitational Waves: Their Form and Effects
  A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property, the second-order solution describing such physical waves is obtained. The effects they produce on free particles are found to consist of nonlinear oscillations along the direction of propagation. 
R. Aldrovandi, J. G. Pereira, Roldao da Rocha, K. H. Vu