  We study the bosonic structure of $F$-term Nambu-Goto cosmic strings forming
in a realistic SO(10) implementation, assuming standard hybrid inflation. We
describe the supersymmetric grand unified theory, and its spontaneous symmetry
breaking scheme in parallel with the inflationary process. We also write the
explicit tensor formulation of its scalar sector, focusing on the
sub-representations singlet under the standard model, which is sufficient to
describe the string structure. We then introduce an ansatz for abelian cosmic
strings, discussing in details the hypothesis, and write down the field
equations and boundary conditions. Finally, after doing a perturbative study of
the model, we present and discuss the results obtained with numerical solutions
of the string structure.
