We present a detailed analysis of the generation and propagation of bright spatial soliton beams in nonlinear Kerr media, in which an input beam is assumed to be of a Gaussian or hyperbolic secant form. The problem is solved by the use of the inverse-scattering transform (IST). The analysis of the discrete spectrum obtained from the direct-scattering problem gives exact information about the parameters of the generated soliton. A condition of soliton appearance in the spectrum as a function of the complex width of the initial Gaussian beam is given numerically. The similarities and differences between the hyperbolic secant and Gaussian beams entering the Kerr medium are analyzed in detail. A case is found in which almost all (approximately 99.5%) the total intensity of the Gaussian beam entering the Kerr medium is transformed into the soliton beam. However, this analogy to the self-trapping of soliton beams occurs for higher total-intensity values than in the case of the soliton input profile. The evolution from the Gaussian to the soliton envelope is studied and the condition of self-trapping in the near field is found. The numerical method based on the IST of the solution to the nonlinear Schrödinger equation is refined.
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