Dark spatial soliton and quasi-soliton by arbitrary initial beam profiles in negative Kerr local and nonlocal medium

In this paper numerically, generation of dark spatial solitons and quasi-solitons in negative Kerr medium which is described by the (1 + 1)-Dimensional local and nonlocal Nonlinear Schrodinger Equation, using arbitrary initial condition field distributions dissimilar to the analytical solution is demonstrated. In the local and nonlocal case, different initial beam profiles with different initial beam-widths are considered, while different response functions of medium and degrees of nonlocality are governing the nonlocality. For the local case extra (lack of) energy in the center of beam profile is released to (absorbed from) the symmetric transversal area of media respectively, until the beam profile self evolves to the fundamental dark soliton with its appropriate amplitude and beam-width of the analytical dark soliton hyperbolic tangent. In the nonlocal case, the beam profile finds some oscillation on beam-width and evolves to a Reversed-Gaussian function, regardless of the nonlocal response function and the degree of nonlocality. By increasing the degree of nonlocality, the evolved beam profile finds the wider beam-width. Analytical formulas for the propagated intensity profile in nonlocal media are given. All the numerical simulations are done by MATLAB program and Split-Step method.