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

摘要

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 Schrodinger equations for broader-banded deep-water waves, originally proposed by Trulsen and coworkers (1996, 2000) [4,5]. 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.