High-order revivable complex-valued hyperbolic-sine-Gaussian solitons and breathers in nonlinear media with a spatial nonlocality

In this paper, based on the nonlocal nonlinear Schrodinger equation, the evolution of complex-valued hyperbolic-sine-Gaussian beams (CVHSGBs) is investigated in nonlinear media with a spatial nonlocality. It is found that the evolution of CVHSGBs is variable depending on the parameters of complex-valued hyperbolic sine function. Choosing special parameters, the pattern of CVHSGBs can keep unchanged during propagation, and they propagate as solitons or breathers. Furthermore, for the general case, the CVHSGB evolutes periodically, and it recovers into its initial pattern at the end of each evolution period, namely it can be revivable periodically, which can be regarded as a generalized high-order breather. A series of analytical expressions are derived to describe the beam evolution, the intensity pattern, the beam spot size, the real beam curvature, etc. Some numerical simulations are also performed to demonstrate the typical evolution properties.