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

We derive a set of two fourth-order coupled nonlinear Schrodinger 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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3598316]