  Rogue waves are solitary waves with extreme amplitudes, which appear to be a
ubiquitous phenomenon in nonlinear wave propagation, with the requirement for a
nonlinearity being their only unifying characteristics. While many mechanisms
have been demonstrated to explain the appearance of rogue waves in a specific
system, there is no known generic mechanism or general set of criteria shown to
rule their appearance. Presupposing only the existence of a nonlinear
Schr\"odinger-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 may explain the appearance of rogue waves
in a large class of systems.
