  In this paper, we study the condition of quasiclassical integrability of
soliton equations. This condition states that the Hamiltonian structure of
equations, which govern propagation of high-frequency wave packets, is
preserved by the dispersionless flow independently of initial conditions. If
this condition is fulfilled, then the carrier wave number of any packet is a
certain function of local values of the dispersionless variables pertained to
the soliton equations under consideration. We show for several examples that
this function together with the dispersion relation for linear harmonic waves
determine the quasiclassical limit of the Lax pair functions in the scalar
representation of the Ablowitz-Kaup-Newell-Segur scheme.

Exactly Solvable and Integrable Systems;Pattern Formation and Solitons