Quantum field scattering theory for the nonlinear Schrödinger equation with repulsive coupling

Nonstationary quantum field scattering theory is constructed for the nonlinear Schrödinger equation with repulsion. Local fields are introduced through the quantum Gel'fand–Levitan–Marehenko equations; the equivalence of the field problem to a set of $N$-particle quantum-mechanical problems with two-body $\delta$-functional potential (coordinate Bethe ansatz) is not used.