  We propose a Lax equation for the non-linear sigma model which leads directly
to the conserved local charges of the system. We show that the system has two
infinite sets of such conserved charges following from the Lax equation, much
like dispersionless systems. We show that the system has two Hamiltonian
structures which are compatible so that it is truly a bi-Hamiltonian system.
However, the two Hamiltonian structures act on the two distinct sets of charges
to give the dynamical equations, which is quite distinct from the behavior in
conventional integrable systems. We construct two recursion operators which
connect the conserved charges within a given set as well as between the two
sets. We show explicitly that the conserved charges are in involution with
respect to either of the Hamiltonian structures thereby proving complete
integrability of the system. Various other interesting features are also
discussed.
