  We investigate nonlinear f(R) theories in the Kaluza-Klein models with
toroidal compactification of extra dimensions. A point-like matter source has
the dust-like equation of state in our three dimensions and nonzero equations
of state in the extra dimensions. We obtain solutions of linearized Einstein
equations with this matter source taking into account effects of nonlinearity
of the model. There are two asymptotic regions where solutions satisfy the
gravitational tests at the same level of accuracy as General Relativity.
According to these asymptotic regions, there are two classes of solutions. We
call these solutions asymptotic latent solitons. The asymptotic latent solitons
from the first class generalize the known result of the linear theory. The
asymptotic black strings and black branes are particular cases of these
asymptotic solutions. The second class of asymptotic solitons exists only in
multidimensional nonlinear models. The main feature for both of these classes
of solutions is that the matter sources have tension in the extra dimensions.
