LINEAR THEORIES, HIDDEN-VARIABLES AND INTEGRABLE NONLINEAR EQUATIONS

Given a theory, described by some equation for a field psi, it may be interesting to study the dependence of psi on some extra variables whi ch do not appear in the equations (the hidden variables). In the case of linear theories, we show that such a dependence is described by int egrable nonlinear equations, which are implicit symmetries of the corr esponding linear equations. In particular, if the order of the equatio ns describing the theory is two, we derive a class of integrable multi dimensional and/or discrete generalizations of the Liouville equation.