##
D.E. Pelinovsky

#
A Mysterious Threshold for Transverse
Instability of Deep-Water Solitons

###
Mathematics and Computers in Simulations 55, 585-594 (2001)

**Abstract:**

Properties of the linear eigenvalue problem associated to a
hyperbolic nonlinear Schrodinger equation are reviewed. The
instability band of a deep-water soliton is shown to merge
to the continuous spectrum of a linear Schrodinger 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.

**Keywords**:

HYPERBOLIC NLS EQUATIONS, WATER-WAVE SOLITONS,
TRANSVERSE INSTABILITY, SCHRODINGER OPERATORS,
PERTURBATION THEORY FOR EMBEDDED EIGENVALUES