Study Of The Propagating Properties Of Spatiotemporal Similaritons And The Interaction Between Similaritons

The dynamical evolution and interaction of (3+1)-dimensional similaritons have been investigated. The influence of dispersion/diffraction, nonlinearity, gain/loss and other parameters on the amplitude, phase, width and chirp of similaritons has been studied. The effects of the nonlinear tunneling on self-similar pulse have been analyzed, with the comparation between dispersion-barrier/well and nonlinear-barrier/well. Based on these results, the parameter modulation and dynamical control on similaritons have been proposed. These provide a relatively reliable theoretical basis for the long-haul telecommunication networks. The main contents are as follows.1. Study in the dynamical control of (3+1)-dimensional spatiotemporal similaritons in inhomogeneous optical fibersA nonlinear Schrodinger equation to (3+1)-dimensional spatiotemporal similaritons has been introduced, which describes the propagation of optical pulses in a cubic-quintic nonlinearity medium with distributed dispersion and gain. By means of F-expansion technique and the similarity reduced method, self-similar cnoidal waves and chirped similariton solutions have been obtained in consideration of the exact balance of dispersion/diffraction, cubic and quintic nonlinearity and the gain/loss. Based on exact solutions, we discussed dynamical evolution behaviors of self-similar cnoidal waves and similaritons in two kinds of typical soliton control systems. By choosing different dispersion/diffraction, nonlinearity and gain/loss parameters, the control and management for the amplitude and width of similaritons have been achieved. With the help of these analytical findings, the potential application of similarions can be found in areas such as optical fiber amplifiers and long-haul telecommunication networks for achieving pulse compression.2. Study in the interaction and dynamical control of (3+1)-dimensional spatiotemporal similaritons in a linear potentialVia the similarity transformation, we investigated the generalized (3+1)-dimensional NLSE with a linear potential and derived a series of analytical spatiotemporal soliton and similariton solutions whose forms depend on the exact balance of the dispersion/diffraction, nonlinearity and the gain or loss. In two different linear potential systems, the dynamical evolution and parameter control of the soliton and similariton have been compared.We analyzed the separating or interacting evolutional behavior of bright and dark similariton pairs under the influence of the parameter control. Through numerical simulations, the anti-noise ability of similaritons has been analyzed.3. Study in the influence on simliations with nonlinear tunneling in optical fibers.We obtained an exact similarity transformation for the (n+l)-dimensional generalized nonlinear Schrodinger equation with varying dispersion/diffraction, nonlinearity and gain/loss. With the help of the similarity transformation, we obtained spatiotemporal similaritons and solitons. We investigated the nonlinear tunneling of the flat-top similariton and compared the effects of dispersion-barrier/well on the similariton with that of nonlinear-barrier/well. The parameter control on the properties of the similariton after passing through the barrier/well has been studied. These results will be useful to the development of high dimensional similariton control technique.