  Temporal optical solitons have been the subject of intense research due to
their intriguing physics and applications in ultrafast optics and
supercontinuum generation. Conventional bright optical solitons result from the
interaction of anomalous group-velocity dispersion and self-phase modulation.
Here we report the discovery of an entirely new class of bright solitons
arising purely from the interaction of negative fourth-order dispersion and
self-phase modulation, which can occur even for normal group-velocity
dispersion. We provide experimental and numerical evidence of shape-preserving
propagation and flat temporal phase for the fundamental pure-quartic soliton
and periodically modulated propagation for the higher-order pure-quartic
solitons. Using analytic theory, we derive the approximate shape of the
fundamental pure-quartic soliton exhibiting excellent agreement with our
experimental observations. Our discovery, enabled by the unique dispersion of
photonic crystal waveguides, could find applications in communications and
ultrafast lasers.
