Coupling-managed criticality in nonlinear dynamics of an integrable exciton-phonon system on a one-dimensional lattice
Oleksiy O. Vakhnenko
Department for Theory of Nonlinear Processes in Condensed Matter, Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, Kyiv 03143, Ukraine
Received April 26, 2021, published online October 25, 2021
A one-dimensional nonlinear dynamical system of coupled intra-site excitations and lattice vibrations is studied. The system as a whole is shown to be integrable in the Lax sense and it admits the exact four-component
analytical solution demonstrating the pronounced mutual influence between the interacting subsystems in the form of essentially nonlinear superposition of two principally distinct types of traveling waves. The inter-play between the coupling strength and the parameter of localization causes the criticality of system’s dynamics manifested as the dipole-monopole transition in the spatial distribution of intra-site excitations.