Asymmetric Shape and Dynamic Stability of Exciton-Phonon Solitons Moving in a Medium

Abstract

Solitons are known to move ballistically through a medium without change of their shape. In practice, the shape of a soliton can change, and a long lasting tail appears behind the soliton moving in a periodic medium. Such a behavior can be described within the model of exciton-phonon coherent states as a dynamic effect in soliton transport. We argue that the coupling between the bosonic excitations of the medium, such as excitons, and the elastic modes of it, such as phonons, can be responsible for these effects. We derive nonlinear dynamic equations for the excited medium in the long wavelength approximation (a generalized Zakharov system) and apply a ballistic ansatz for the coherent state of bosons and displacement field (a kind of the condensate in this model). Like solitons, the quasistationary solution we obtained can move through the medium ballistically. Unlike solitons and kinks, there are inhomogeneous corrections to the ballistic velocity and coherent phase of the condensate that control the change of the packet shape. In the limit of T → 0, laws of conservation prescribe formation of the cloud of collective excitations around the quasistationary Bose-core of the packet so that the density of the boson-phonon tail behind the moving coherent part can be estimated at any given t. The total packet can be associated with an exciton-phonon comet with the quasistable coherent Bose-nucleus and incoherent tail moving in the medium.