Dipole–monopole alternative in nonlinear dynamics of an integrable gauge-coupled exciton-phonon system on a one-dimensional lattice
Department for Theory of Nonlinear Processes in Condensed Matter, Bogolyubov Institute for Theoretical Physics, The National Academy of Sciences of Ukraine, 14-B Metrologichna Street, 03143, Kyïv, Ukraine
2 Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyïv, 4-D Akademika Hlushkova Avenue, 03680, Kyïv, Ukraine
Accepted: 27 September 2022
Published online: 25 October 2022
The gauge-coupled nonlinear dynamical system of -symmetric intra-site excitations and lattice vibrations on a one-dimensional lattice is studied. The system proves to be integrable in the Lax sense inasmuch as it admits the semi-discrete zero-curvature representation associated with the specific auxiliary linear problem of third order. The appropriate Darboux–Bäcklund technique for generating the system’s nontrivial solutions is developed and thoroughly explained. In the framework of this approach both the singular and physically meaningful four-component solutions are found analytically. The physically meaningful four-component solution is shown to demonstrate the dipole–monopole alternative in nonlinear dynamics of pseudo-excitonic subsystem caused by the interplay between the two typical spatial scales. These spatial scales characterize the spatial arrangements of two principally distinct types of traveling waves in their essentially nonlinear superposition. The criterion of critical transition between the dipole and monopole regimes in the spatial distribution of intra-site excitations is established. The under-critical and over-critical regimes of system’s dynamics are comprehensively illustrated graphically.
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