| When the Inverse Scattering Technique (IST) is applied with the purpose of detection of
solitary deep-water wave groups hidden in the field of irregular waves, then the determination
of the carrier wavenumber, k0, is one of the most important steps. It is because the
dominant wave length introduces a characteristic scale in the system. The similarity
parameter of the nonlinear Schrodinger equation (equivalent of the Benjamin –
Feir Index), which characterizes the role of nonlinear effects in comparison to the
wave dispersion, is dimensional as [m2]. In fact, an error in the value of the carrier
wavenumber results in an error in evaluation of the solitary group amplitude with
factor 2. When waves are not very small, and their spectrum is not very narrow, the
problem how to calculate the carrier wavenumber becomes crucial. In this study we
consider a number of approaches to calculate k0 on the basis of given examples
of momentary snapshots of the surface displacement, looking for the most robust
methods. Finally, we suggest a different approach, of a two-step IST procedure, when
the carrier wavenumber at the second step is corrected according to the result of
analysis at the first step. We show that this approach possesses improved robustness
and is much less dependent on the way how the primary value of k0 is evaluated. |