Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water

Starting from the Hamiltonian formulation of the water wave problem and using the approach recently developed by Craig et al. (2010) [8], we derive Hamiltonian versions of the higher-order nonlinear Schrödinger equations for broader-banded deep-water waves, originally proposed by Trulsen and co-workers (1996, 2000) [4] and [5]. A Benjamin–Feir stability analysis is performed and shown to be in good agreement with previous work. Numerical simulations using a symplectic time integration scheme are also presented to illustrate the performance of these new models with regards to their conservative and Benjamin–Feir stability properties.