Nonlinear integrable dynamics of coupled vibrational and intra-site excitations on a regular one-dimensional lattice

• Published in: Physics letters. A 2021-07, Vol.405, p.127431, Article 127431
• Main Author: Vakhnenko, Oleksiy O.
• Format: Article
• Language: English
• Subjects: Coupled nonlinear wave packet; Darboux–Bäcklund transformation; Dirac metamaterials; Exciton-phonon interaction; Monopole-to-dipole crossover; Semi-discrete integrable system
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2021.127431

•Nonlinear integrable exciton-phonon system on a one-dimensional lattice is considered.•Darboux–Bäcklund dressing technique to the system's integration is developed.•Four-component analytical solution to the nonlinear integrable exciton-phonon system is found.•The exciton subsystem is shown to be critical against the value of localization parameter.•Criticality causes crossover between the monopole and dipole regimes of exciton dynamics. The nonlinear integrable system of coupled vibrational and intra-site excitations on a regular one-dimensional lattice is studied analytically in the framework of specially developed Darboux–Bäcklund dressing technique. The obtained four-component solution to the system demonstrates the pronounced mutual influence between the subsystems in the form of essentially nonlinear superposition of two principally distinct types of traveling waves. The solution is shown to be critical against the value of localization parameter, so that in under-critical region the subsystem of intra-site excitations should be treated as an extended monopole whereas in over-critical region – as an extended dipole.