A mysterious threshold for transverse instability of deep-water solitons

Properties of the linear eigenvalue problem associated to a hyperbolic non- linear Schrodinger equation are reviewed. The instability band of a deep-wa ter soliton is shown to merge to the continuous spectrum of a linear Schrod inger operator. A new analytical approximation of the instability growth ne ar a threshold is derived by means of a bifurcation theory of weakly locali zed wave functions. (C) 2001 Published by Elsevier Science B.V. on behalf o f IMACS.