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. 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.
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Funding: The work of A. B. was supported by the Russian Science
Foundation (Grant No. 17-72-30006). S. K. T. acknowledges support by the EU project HALT and the Isaac Newton Institute for Mathematical Sciences, Cambridge within the programme HYD2.