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