Fourth-order perturbative equations in Lagrangian perturbation theory
  for a cosmological dust fluid
  We have derived fourth-order perturbative equations in Lagrangian
perturbation theory for a cosmological dust fluid. These equations are derived
under the supposition of Newtonian cosmology in the
Friedmann-Lema\^{i}tre-Robertson-Walker Universe model. Even if we consider the
longitudinal mode in the first-order perturbation, the transverse mode appears
in the third-order perturbation. Furthermore, in this case, six
longitudinal-mode equations and four transverse-mode equations appear in the
fourth-order perturbation. The application of the fourth-order perturbation
leads to a precise prediction of the large-scale structure.
