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Spontaneous creation of solitons in quadratic media by the downconversion, i.e., parametric instability against the generation of fundamental-frequency excitations, from the truncated Airy-wave (AW) mode in the second-harmonic component is studied. Parameter regions are identified for the generation of one, two, and three solitons, with additional small-amplitude jets. Shares of the total power carried by individual solitons are found. Also considered are soliton patterns generated by the downconversion from a pair of AWs bending in opposite directions.
Conversion of truncated Airy waves (AWs) carried by the second-harmonic (SH) component into axisymmetric $chi^{2}$ solitons is considered in the 2D system with the quadratic nonlinearity. The spontaneous conversion is driven by the parametric instabi
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as sing
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in spatially e
We have investigated the propagation dynamics of the circular Airy Gaussian vortex beams (CAGVBs) in a (2+1)-dimesional optical system discribed by fractional nonlinear Schrodinger equation (FNSE). By combining fractional diffraction with nonlinear e
The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framew