Abstract A general method to construct basis functions for fermionic systems which account for the SU(2) symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system and it appears as a natural generalization of the Bethe Ansatz to the case of non integrable systems. As an example we present the block diagonalizati...

This paper obtains the soliton solution for the Calogero–Degasperis and the potential Kadomtsev–Petviashvili equations. The tanh–coth and the tan–cot methods are used to retrieve the solutions. Finally, the ansatz method is also used to integrate these equations with any arbitrary constant coefficients. Finally, a fewnumerical simulations are also given. © 2011 Elsevier Ltd. All rights reserved.

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups Eτ,η(glN). The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.