  A generic novel model governing optical pulse propagation in a nonlinear
dispersive amplifying medium with asymmetric (linear spectral slope) gain is
introduced. We examine the properties of asymmetric optical pulses formed in
such gain-skewed media, both theoretically and numerically. We derive a
dissipative optical modification of the classical shallow water equations that
highlights an analogy between this phenomenon and hydrodynamic wave-breaking.
We observe the development of spectral optical shock waves, and discuss the
conditions and origins of this spectral wave-breaking in media with asymmetric
gain. These findings provide insight into the nature of asymmetric optical
pulses capable of accumulating large nonlinear phase without wave-breaking, a
crucial aspect in the design of nonlinear fiber amplifiers.
