Hierarchy of integrable Hamiltonians describing the nonlinear n-wave interaction

In the paper, we construct a hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in a nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic functions of the first kind. These solutions can be used to study such physical phenomena as the Kerr effect or parametric conversion.