We simulate and analyze the propagation of truncated temporal Airy pulses in a single mode fiber in the presence of self-phase modulation and anomalous dispersion as a function of the launched Airy power and truncation coefficient. Soliton pulse shedding is observed, where the emergent soliton parameters depend on the launched Airy pulse characteristics. The Soliton temporal position shifts to earlier times with higher launched powers due to an earlier shedding event and with greater energy in the Airy tail due to collisions with the accelerating lobes. In spite of the Airy energy loss to the shed Soliton, the Airy pulse continues to exhibit the unique property of acceleration in time and the main lobe recovers from the energy loss (healing property of Airy waveforms).

We investigate and analyze temporal soliton interactions with a dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center wavelength (or frequency), via split step Fourier numerical simulation. Truncated Airy pulses, which remain self-similar during propagation and have a ballistic trajectory in the retarded time frame, can interact with a nearby soliton by its accelerating wavefront property. We find by tracking the fundamental parameters of the emergent soliton-time position, amplitude, phase and frequency-that they alter due to the primary collision with the Airy main lobe and the continuous co-propagation with the dispersed Airy background. These interactions are found to resemble coherent interactions when the initial time separation is small and incoherent at others. This is due to spectral content repositioning within the Airy pulse, changing the nature of interaction from coherent to incoherent. Following the collision, the soliton intensity oscillates as it relaxes. The initial parameters of the Airy pulse such as initial phase, amplitude and time position are varied to better understand the nature of the interactions.

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