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We investigate in detail the qualitative similarities between the pulselocalization characteristics observed using sinusoidal phase modulation duringlinear propagation and those seen during the evolution of Akhmediev breathersduring propagation in a system governed by the nonlinear Schr{\"o}dingerequation. The profiles obtained at the point of maximum focusing indeed presentvery close temporal and spectral features. If the respective linear andnonlinear longitudinal evolutions of those profiles are similar in the vicinityof the point of maximum focusing, they may diverge significantly for longerpropagation distance. Our analysis and numerical simulations are confirmed byexperiments performed in optical fiber.

Akhmediev breather signatures from dispersive propagation of a periodically phase-modulated continuous wave