Bäcklund transformations and soliton-type solutions for σ models with values in real Grassmannian spaces

A Bäcklund transformation for the two-dimensional σ model with values in oriented real Grassmannian spaces is constructed using the known Bäcklund transformation for the SO(n) principal models. The construction provides a natural way to linearize the differential system of the Bäcklund transformation. In the case of the S ⁿ≈SO(n+1/SOn) model, the Backlund transformation reduces to that of Pohlmeyer. The one-soliton solution for S ²～SO(3)/SO(2) is obtained analytically and plots of one-soliton and two-soliton solutions are displayed.