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acoustic amplitude Ansatz antikink approximation associated Baeriswyl benzene bipolarons bond alternation bond length bond order bond-bond polarizability boundary conditions Brazovskii and Kirova calculations Campbell and Bishop charged kinks conducting polymers conduction band configuration conjugation continuum limit continuum model corresponds Coulomb coupling limit cut-off defect structures density described determined dimerization domain-walls doped dynamical matrix effects elastic energy electron correlation exciton Fermi force constant function gap equation ground Hamiltonian Hartree-Fock Hellmann-Feynman theorem Hiickel model impurity instability interchain coupling ir-electrons kink kink defect kink-antikink pair Kivelson levels Maki mean-field Mele and Rice midgap modes neighbouring neutral kinks obtained odd-numbered chain optical absorption optical gap order parameter phase diagram phonon polaron polyacetylene polypyrrole represents resonance integrals respect Schrieffer Section self-consistency condition self-consistency equation singly occupied soliton solution spectrum spin symmetry temperature total energy trans-polyacetylene valence band weak coupling weak-coupling limit yields