General soliton and polaron solutions in the continuum polyacetylene model through inverse scattering technique

The continuum model of dimerized polyacetylene (CH)x is reduced to the Zakharov-Shabat (ZS) spectral problem and their correspondence is analysed. This helps to find through the inverse scattering technique the topological as well as the nontopological general soliton and polaron solutions to the polyacetylene model. The self-consistency condition, on the other hand, restricts the class of admitted solutions constrained by the ‘color’ degrees of freedom of the electron wave functions. As a result in a standard single-chain polyacetylene, the allowed solutions are only a kink, a polaron and a new kink-polaron state. However, in a multi-chained version of polyacetylene a rich set of general solutions is possible to exist depending on the number of chains.