2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124648We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality Catastrophe} or {boundary states} with the $τ$-function of the modified KP-hierarchy. The established relation allows to apply the apparatus of soliton theory to the study of non-linear aspects of quantum dynamics. We also describe a {\it bosonization in momentum space} - a representation of a fermion operator by a Bose field in the presence of a boundary state.Some corrections madeExactly Solvable and Integrable SystemsOther Condensed MatterHigh Energy Physics - Theorytext