Dipole–monopole alternative as the precursor of pseudo-excitonic chargeless half-mode in an integrable nonlinear exciton–phonon system on a regular one-dimensional lattice

The new form of an integrable exciton–phonon nonlinear dynamical system distinguished by the two physical 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 analytical four-component solution to the system’s dynamical equations found by means of Darboux–Bäcklund dressing technique turns out to be of broken PT-symmetry giving rise to the crossover between the monopole and dipole regimes of system’s dynamics. The crossover effect is proved to be inseparable from the mutual influence between the interacting subsystems in the form of specific nonlinear superposition of two qualitatively distinct types of traveling waves characterized by the two spatial scales and by the two velocities of two physically distinct origins. The threshold value of localization parameter separating the monopole and dipole dynamical regimes is strictly established in terms of the basic physical parameters. The phenomenon of dipole–monopole alternative for the spatial distribution of pseudo-excitons is shown to initiate the partial splitting between the pseudo-excitonic and vibrational subsystems in the so-called threshold dynamical regime specified by the threshold value of localization parameter. This partial splitting is manifested by the complete elimination of one pseudo-excitonic component accompanied by the actual conversion of another pseudo-excitonic component into the pseudo-excitonic chargeless half-mode. Relying upon the inherent PT-symmetry of system’s dynamical equations the four-component symmetry broken PT-conjugated counterpart solution is also analytically recovered. The integrable nonlinear exciton–phonon system under study is expected to be useful in modeling the nonlinear dynamical properties of PT-symmetric metamaterials. The critical overviews of several relevant and several irrelevant model systems are given to rebuff certain misleading but dogmatically accepted notions and statements circulating in scientific literature.