Comment on "Triggering Rogue Waves in Opposing Currents"

Abstract

The authors of a recent Letter ([1] M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011)) based their study of rogue waves in nonuniform currents on a modified nonlinear Schr\"odinger equation (NLSE; see Eq.(1) in [1]). However, I show here that equation is not correct. It gives wrong solutions even in the first order on the supposedly small parameter $U/c_{\rm g}$, where $U(x)$ is a current, and $c_{\rm g}=g/(2 \omega)$ [here $\omega$ is a mean frequency of a quasi-monochromatic wave train, and $g$ is the gravity acceleration]. I also suggest an accurate variant of NLSE, valid in the presence of a large-scale nonuniform current under condition $(1+4\omega U/g) \gtrsim 0.2$.