  Dynamics of ideal fluid with free surface can be effectively solved by
perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that
perturbation theory, which includes third and fourth order terms in the
Hamiltonian, results in the ill-posed equations because of short wavelength
instability. To fix that problem we introduce the canonical Hamiltonian
transform from original physical variables to new variables for which
instability is absent.
