| Abstract: |
| We investigate unidirectional reductions of deep-water evolution equations without recourse to Fourier normal variables or complex canonical transformations. By closing the system entirely in terms of surface elevation, we obviate the need for velocity potential initial data, which is a significant advantage for simulating coherent structures such as breathers from experimental observations. The resulting non-local equations retain the exact linear dispersion relation and capture leading-order cubic nonlinearities. We show that both Hamiltonian and non-Hamiltonian models can be consistently formulated within this framework. Notably, lower-accuracy Hamiltonian variants reveal an unexpected integrable structure, while non-Hamiltonian versions achieve remarkable accuracy against fully nonlinear Euler computations up to moderate steepness. All models reduce to the nonlinear Schrodinger equation in the narrow-band limit with the correct deep-water coefficients. |
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