Allayarov M., Tsoy E. N. Dynamics of Airy beams in nonlinear media. // Phys. Rev. A, V. 90, 023852 (2014).

The dynamics of truncated Airy beams in optical media with Kerr nonlinearity is studied in the framework of the nonlinear Schrödinger (NLS) model. It is demonstrated that an intense Airy beam with zero total momentum can generate static solitons, as well as moving solitons. The parameters of these solitons are calculated using the Zakharov-Shabat scattering problem associated with the NLS equation. It is found that solitons take the main part of the initial power, while only a small fraction of the power is transformed into a self-accelerating linear packet. The threshold parameters of the Airy beam for the soliton formation are obtained. It is shown that the threshold for the formation of the first static soliton is also a threshold of the solitonless regime.