Non-perturbative solution of nonlinear Heisenberg equations

A new non-perturbative method of solution of the nonlinear Heisenberg equations in a finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schr¨ odinger picture method, is based on a finite operator expansion into the elementary processes. It provides us with insight into the nonlinear quantal interaction from a different point of view. Thus, one can investigate the nonlinear system in both pictures of quantum mechanics.