The dressing chain of discrete symmetries and proliferation of nonlinear equations (Q1567989)

This paper deals with a direct method for using dressing chains to proliferate integrable equations. As paradigms to model equations the authors consider KdV and sine-Gordon (SG) equations and explain an algorithm that allows the construction of a new integrable system and its L-A pair from a known L-A pair and the discrete symmetry. The main result of this paper is the construction of an irreducible representation for the rotation group using positive normalized probability distribution functions \(w^j(i,u)\) for the spin projections \(i\) on the quantization axis defined by the normal to the unit sphere.