Solitons in the Peierls condensate. II. Amplitude solitons

Charge-density waves whose phase is constrained have amplitude solitons. Exact soliton and soliton lattice solutions for an electron-phonon system in one dimension are constructed by a mapping into the sine-Gordon system. The method is extended to systems with an extrinsic gap parameter as in (AB)ₓ polymers. Soliton-soliton interactions in the continuum limit are exponential and repulsive. Discrete lattice effects lead to competing interactions which decay as the inverse distance: an attractive force from the finite momentum cutoff and a (usually stronger) repulsive force from coupling with acoustic phonons.