A mysterious threshold for transverse instability of deep-water solitons

Properties of the linear eigenvalue problem associated to a hyperbolic non-linear Schrödinger equation are reviewed. The instability band of a deep-water soliton is shown to merge to the continuous spectrum of a linear Schrödinger operator. A new analytical approximation of the instability growth near a threshold is derived by means of a bifurcation theory of weakly localized wave functions.