Intertwining operators and the quantum inverse method for the non-linear Schrödinger equation

We consider the quantum non-linear Schrödinger equation as a quantum field model in 1 + 1 space-time. It has been recently solved by the quantum inverse method and by the method of intertwining operators. Expressions obtained by the two methods are formally different. We show here that nevertheless these expressions defined the same operators on Fock space. Thus both methods are correct. Using them together provides a new insight into the quantum non-linear Schrödinger equation.