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- W4322743412 abstract "We develop a general framework to describe the cubically nonlinear interaction of a unidirectional degenerate quartet of deep-water gravity waves. Starting from the discretised Zakharov equation, and thus without restriction on spectral bandwidth, we derive a planar Hamiltonian system in terms of the dynamic phase and a modal amplitude. This is characterised by two free parameters: the wave action and the mode separation between the carrier and the side-bands. The mode separation serves as a bifurcation parameter, which allows us to fully classify the dynamics. Centres of our system correspond to non-trivial, steady-state nearly-resonant degenerate quartets. The existence of saddle-points is connected to the instability of uniform and bichromatic wave trains, generalising the classical picture of the Benjamin-Feir instability. Moreover, heteroclinic orbits are found to correspond to primitive, three-mode breather solutions, including an analogue of the famed Akhmediev breather solution of the nonlinear Schrodinger equation." @default.
- W4322743412 created "2023-03-03" @default.
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- W4322743412 date "2023-03-01" @default.
- W4322743412 modified "2023-10-14" @default.
- W4322743412 title "The nonlinear Benjamin–Feir instability – Hamiltonian dynamics, discrete breathers and steady solutions" @default.
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- W4322743412 doi "https://doi.org/10.1017/jfm.2023.96" @default.
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