A Lax pair for the characteristic equations of averaged multi-particle operators (Q1582841)

The authors study a system of two nonlinear integro-differential equations for the characteristics of an averaged fermionic operator corresponding to a multi-particle Hamiltonian \(H= \sum_j T_j+ \sum_{j<k} V_{j,k}\) where \(T_j\) is the integral kernel of the Hamiltonian of a single particle and \(V_{j,k}\) is the integral kernel of the pair interaction operator. Generalizing a result of \textit{Yu. I. Manin} [Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 11, 5-152 (1978; Zbl 0413.35001)] on the corresponding Lax pair for a special choice of \(T_j\) and \(V_{j,k}\), the authors construct a Lax pair for the equations mentioned above in the general case.