Analysis of the Nonlinear Spectrum of Intense Sea Wave with the Purpose of Extreme Wave Prediction

Direct scattering transform: catch soliton if you can

“…3(b) shows that for large enough L these deviations in eigenvalues lead to the exponential growth of errors as predicted by the developed theory, see Eq. (16). At the same time, for smaller L < 15, as expected, we observe the truncation errors for the norming constants.…”

“…The Boffetta-Osborne method [7] represents the first numerical realization of the DST followed by a sequence of further improvements and alternatives [8][9][10][11][12]. These advancements have made the DST an essential scientific tool with a wide range of theoretical and experimental applications [4,[13][14][15][16][17]. The remarkable ability of the DST to identify and characterise solitons representing the coherent structures in nonlinearly interacting wave fields provides fundamental information about the origin of various physical effects [18,19] and can be fruitfully used in practical applications such as optical telecommunication systems [20][21][22][23].…”

“…The remarkable ability of the DST to identify and characterise solitons representing the coherent structures in nonlinearly interacting wave fields provides fundamental information about the origin of various physical effects [18,19] and can be fruitfully used in practical applications such as optical telecommunication systems [20][21][22][23]. A significant amount of work has been devoted to understand the distribution of soliton amplitudes and velocities (eigenvalues) [24,25] with particular focus on its role in propagation of ocean waves [16,21,26] and optical pulses [18,27].…”

Persistence of hydrodynamic envelope solitons: detection and rogue wave occurrence

“…In Sec. IV we analyze the realization No 295 by means of the own method of evaluation of the soliton content suggested in [20,35] and further improved in [21]. The method employs the Inverse Scattering Transform for the NLS equation, formulated in infinite line and allows estimation of the amplitudes, velocities and locations of the soliton groups.…”

“…In the present work we reconsider our observation of long-living wave groups in the numerical simulation of irregular sea waves and discuss their nature on a more solid background. We apply the nonlinear analysis based on the Inverse Scattering Transform (IST) [20,21] which helps to reveal the soliton-type nonlinear groups and to estimate them quantitatively.…”