Fourth-order coupled nonlinear Schrödinger equations for gravity waves on deep water

Abstract

We derive a set of two fourth-order coupled nonlinear Schrödinger equations describing the evolution of two two-dimensional systems of deep-water gravity waves with different wavenumbers or directions of propagation. It is shown that the coupled equations can be formulated as a Hamiltonian system and that they conserve the total wave action and momentum of the combined wave field. The modulational instability of two interacting uniform wave trains is considered. © 2011 American Institute of Physics.