Hidden Symmetries of the Principal Chiral Model Unveiled
  By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all known `hidden symmetries' and B\"acklund transformations, as well as a host of new symmetries, arise. 
C. Devchand and Jeremy Schiff