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Abstract
The behaviour of the Peregrine breather-type rogue waves is numerically studied based on the fourth-order nonlinear Schrödinger equation. The wavelet analysis method is adopted in order to analyse the time-frequency energy distribution during the generation and evolution of the Peregrine breather. It shows that the peak of the largest amplitudes of the resulting waves can be described in terms of the Peregrine breather-type solution and leads to the solution of the nonlinear Schrödinger (NLS) equation. Meanwhile, strong energy density is found to surge instantaneously and be seemingly carried over to the high-frequency components at the instant when the large, rogue wave occurs.
Disclosure statement
No potential conflict of interest was reported by the authors.
Nomenclature
| ϕ | = | Velocity potential (m2/s) |
| ζ | = | Wave surface elevation (m) |
| ϕ | = | Velocity potential of mean flow (m2/s) |
| ζ | = | Wave surface elevation of mean flow (m) |
| A,A2,A3 | = | Complex displacement amplitudes (m) |
| B,B2,B3 | = | Complex velocity potential amplitudes (m2/s) |
| k | = | Wave number (m−1) |
| ω | = | Wave frequency (s−1) |
| cg | = | Wave group velocity (m/s) |
| x | = | Real space variable (m) |
| t | = | Real time variable (s) |
| a | = | Wave amplitude (m) |
| γ | = | Scale factor |
| ϵ | = | Wave steepness |
| ξ | = | Dimensionless time variable |
| η | = | Dimensionless space variable |
| Ψ | = | Phase function |
| υ | = | Fourier mode |
| q | = | Dimensionless complex wave amplitude |
| X | = | Dimensionless time variable |
| T | = | Dimensionless space variable |
| Ω, p, β | = | Intermediate variables |