Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction

TL;DR

This paper develops a hierarchy of integrable Hamiltonian systems to model nonlinear n-wave interactions in dielectric media, providing exact solutions for specific cases using elliptic functions.

Contribution

It introduces a new hierarchy of Hamiltonians for nonlinear wave interactions and derives exact solutions for particular cases.

Findings

Hierarchy of integrable Hamiltonians constructed

Exact solutions expressed via elliptic functions

Applicable to nonlinear dielectric media

Abstract

In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic functions of the first kind.