The travelling wavelets approach to gravitational instability theory: one-dimensional wavelets

We apply the travelling wavelets method to gravitational instability theory for the investigation of large-scale structure formation in cosmology. As the first step of our approach, the method is first applied to the 1D cosmo logical Euler-Poisson equation system. We test the stability of the linear (evolution) regime in this plane-symmetric case. As a result, our analysis confirms the existence of the linear regime for some configurations of fiel ds describing the evolution of cosmological structures. Moreover, it provid es us with estimates for the delay needed for structures of given scale and magnitude to deviate from the linear regime. We also exhibit other configu rations for which the linear. approximation is not valid nt any time. In pa rticular, density defaults (i.e. holes) turn out to be highly non-linear st ructures that dominate the evolution.