Dipole–Monopole Crossover and Chargeless Half-Mode in an Integrable Exciton–Phonon Nonlinear Dynamical System on a Regular One-Dimensional Lattice

Abstract

A new form of the integrable nonlinear exciton–phonon dynamical system characterized by two physically independent parameters is suggested. The system is settled along an infinite one-dimensional regular lattice, and it admits the semi-discrete Lax representation in terms of 3 × 3 auxiliary spectral and evolution matrices. The explicit analytic four-component solution to the system’s dynamical equations found by means of the Darboux–Backlund dressing technique turns out to be of broken PT-symmetry. Each component of the solution consists of two nonlinearly superposed traveling waves that inspires the dipole–monopole crossover for the equal values of two physically distinct spatial scaling parameters of the nonlinear wave packet. The phenomenon of the dipole–monopole alternative for the spatial distribution of pseudoexcitons is shown to initiate the partial splitting between the pseudoexcitonic and vibrational subsystems at the threshold point manifested by the complete elimination of one pseudoexcitonic component and the conversion of another pseudoexcitonic component into the pseudoexcitonic chargeless half-mode.