16.1. Backlund transformations

a. Write down the Backlund transformations for the Sine–Gordon model.

b. Taking as initial solution of the equation of motion φ = 0, determine the new solution ˆ φ(z, ¯ z) and show that it coincides with the solitonic solution of the model.

c. Iterate the procedure to determine the other classical solutions of the Sine–Gordon model.