Darboux transformation and exact solutions for the model ofcylindrically symmetrical chiral field

摘要

The application of the Darboux transformation method to theintegrable model of a cylindrically symmetrical chiral field has beenconsidered. The associated linear system of matrix equations has beenproposed and the properties of symmetry for its solution obtained. Thenecessary form of Darboux transformation has been found and formal one-and N-soliton solutions constructed. With the use of Polhmayer'stransformation, a sine-Gordon type equation has been given and anhypothesis about its integrability proposed