The application of the Darboux Transformation method to the integrable modelof Cylindrically Symmetrical Chiral field has been considered. The associatedlinear system of matrix equations has been proposed and the properties ofsymmetrie for its solutions has been obtained. The necessary form of DarbouxTransformation has been found and formal one- and N-soliton solutions have beenconstructed. With the use of Pohlmayer's Transformation the equation sin-Gordontype have been given and the hypothesis about its integrability has beendeduced.
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