Partially "invisible"pulsation of asymmetric soliton molecules

Pulsation is a universal phenomenon in all disciplines of nonlinear science, which generally exhibit various nonlinear soliton dynamic modes in nonlinear optics. With the emergence of real-time spectral measurement technology, a new phenomenon of optical soliton pulsation, "invisible"soliton pulsation, has gradually attracted researchers' attention. In this paper, by solving the coupled Ginzburg-Landau equation, we have discovered the partially "invisible"pulsation phenomenon of asymmetric soliton molecules (SMs) composed of two unequal -intensity pulses in a normal -dispersion Mamyshev oscillator for the first time. It is indicated that the fluctuation periods of each internal pulse in asymmetric SMs in terms of peak power, energy, and relative phase difference are all four roundtrips. However, the oscillation period of asymmetric SMs energy is two roundtrips, only half of the above period. Further research shows that the oscillation of the relative phase difference between two internal pulses in SMs is related to the variation of their intensity difference, which can also affect the position change of the spectral modulation peak. This work will enrich the research on "invisible"soliton pulsation and is of great significance for promoting the development of nonlinear dissipative systems.