One-dimensional two-component Bose gas and the algebraic Bethe ansatz

We apply the nested algebraic Bethe ansatz to a model of a one-dimensional two-component Bose gas with a $\delta$-function repulsive interaction. Using a lattice approximation of the $L$-operator, we find the Bethe vectors of the model in the continuum limit. We also obtain a series representation for the monodromy matrix of the model in terms of Bose fields. This representation allows studying an asymptotic expansion of the monodromy matrix over the spectral parameter.