  New analytical solutions for gravity, scalar and vector field localization in
Randall-Sundrum(RS) models are found. A smooth version of the warp factor with
an associated function $f(z)=\exp(3A(z)/2)$ inside the walls ($|z|<d$) is
defined, leading to an associated equation and physical constraints on the
continuity and smoothness of the background resulting in a new space of
analytical solutions. We solve this associated equation analytically for the
parabolic and P\"oschl-Teller potentials and analyze the spectrum of resonances
for these fields. By using the boundary conditions we are able to show that,
for any of these solutions, the density probability for finding a massive mode
in the membrane has a universal behavior for small values of mass given by
$|\psi_m(0)|^2=\beta_1m+\beta_3m^3+\beta_L m^3\log(m)+\cdots$. As a
consequence, the form of the leading order correction, for example, to the
Newton's law is general and does not depend on the potential used. At the end
we also discuss why complications arises when we try to use the method to find
analytical solutions to the fermion case.
