Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
Rogue waves, by definition, are rare events of extreme amplitude, but
at the same time they are frequent in the sense that they can exist in a wide
range of physical contexts. While many mechanisms have been demonstrated to
explain the appearance of rogue waves in various specific systems, there is
no known generic mechanism or general set of criteria shown to rule their
appearance. Presupposing only the existence of a nonlinear Schrödinger-type
equation together with a concave dispersion profile around a zero dispersion
wavelength we demonstrate that solitons may experience acceleration and
strong reshaping due to the interaction with continuum radiation, giving rise
to extreme-value phenomena. The mechanism is independent of the optical Raman
effect. A strong increase of the peak power is accompanied by a mild increase
of the pulse energy and carrier frequency, whereas the photon number of the
soliton remains practically constant. This reshaping mechanism is
particularly robust and is naturally given in optics in the supercontinuum
generation process