  We construct the new one-dimensional Dirac Hamiltonians that are spectrally
isomorphic (not isospectral) with the known exactly solvable models. Explicit
formulas for their spectra and eigenstates are provided. The operators are
utilized for description of Dirac fermions in graphene in presence of an
inhomogeneous electromagnetic field. We discuss explicit, physically relevant,
examples of spectrally isomorphic systems with both non-periodic and periodic
electromagnetic barriers. In the latter case, spectrally isomorphic two- and
three-gap systems associated with the Ablowitz-Kaup-Newell-Segur hierarchy are
considered.
