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Dipole–monopole alternative in nonlinear dynamics of an integrable gauge-coupled exciton-phonon system on a one-dimensional lattice

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Abstract

The gauge-coupled nonlinear dynamical system of \({\mathcal {P}}{\mathcal {T}}\)-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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Acknowledgements

The work has been supported by the National Academy of Sciences of Ukraine within the Project No 0122U002279 (Conformational mechanics of DNA macromolecule under the influence of biologically active molecules and ions). The Authors are thankful to the Reviewer for the suggestion to provide the physical background of the nonlinear dynamical system under study. The Authors are greatly indebted to Dr. Olga Kocherga for the valuable recommendations on English grammar.

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  1. 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, Kyïv, 03143, Ukraine

    Oleksiy O. Vakhnenko

  2. Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyïv, 4-D Akademika Hlushkova Avenue, Kyïv, 03680, Ukraine

    Andriy P. Verchenko

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Oleksiy O. Vakhnenko: Analytical calculations. Andriy P. Verchenko: Computer calculations.

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Vakhnenko, O.O., Verchenko, A.P. Dipole–monopole alternative in nonlinear dynamics of an integrable gauge-coupled exciton-phonon system on a one-dimensional lattice. Eur. Phys. J. Plus 137, 1176 (2022). https://doi.org/10.1140/epjp/s13360-022-03335-w

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