Third-order perturbative solutions in Lagrangian perturbation theory with pressure. II. Effect of the transverse modes

Lagrangian perturbation theory for cosmological fluid describes structure formation in the quasinonlinear stage well. In a previous paper, we presented a third-order perturbative equation for Lagrangian perturbation with pressure. There we considered only the longitudinal modes for the first-order perturbation. In this paper, we generalize the perturbation, i.e., we consider both the longitudinal and the transverse modes for the first-order perturbation. Then we derive third-order perturbative equations and solutions.