  We use the optimal fluctuation method to find the density of electron states
inside the pseudogap in disordered Peierls chains. The electrons are described
by the one-dimensional Dirac Hamiltonian with randomly varying mass (the
Fluctuating Gap Model). We establish a relation between the disorder average in
this model and the quantum-mechanical average for a certain double-well
problem. We show that the optimal disorder fluctuation, which has the form of a
soliton-antisoliton pair, corresponds to the instanton trajectory in the
double-well problem. We use the instanton method developed for the double-well
problem to find the contribution to the density of states from disorder
realizations close to the optimal fluctuation.
