Evolution and collapse of a Lorentz beam in Kerr medium

The effect of Kerr nonlinearity on a Lorentz beam is investigated by using the nonlinear Schrodinger (NLS) equation. Based on the variational method, the evolution of a Lorentz beam in a Kerr medium is demonstrated and the critical collapse powers of the Lorentz beam are derived. Numerical simulations of the propagation of a Lorentz beam in a Kerr medium show that the beam becomes quasi-circular in a very short distance. Although the beam width of the Lorentz beam broadens, the central part of the beam give rise to a partial collapse