Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons

Abstract

Similarity transformation and Hirota bilinearization are deployed to derive exact bright and dark ultrashort one-and two-similariton solutions of a nonautonomous cubic-quintic nonlinear Schrödinger equation. Such wave packets may emerge when group-velocity dispersion and cubic-quintic self-phase modulations are balanced by Raman self-frequency shift in the presence of an external harmonic trap and linear gain or loss. The solutions presented here can be used to investigate the compression, amplification and interaction phenomena associated with bright and dark similaritons in inhomogeneous fiber systems. Furthermore, the dynamics of the characteristic parameters of the similaritons are studied analytically, and similariton stability in a distributed system is tested through extensive computations. As an example application, the tunneling behavior of bright and dark similaritons through cascade dispersion barriers and dispersion wells on an exponential background is investigated, and some interesting novel features are uncovered which are expected to facilitate the control of bright and dark ultrashort similariton in experimental scenarios. Keywords two-similariton, interaction, Raman effect, harmonic potential, cascade tunneling () () () () () () () 0 zz z z w z z w z z p z z w z

Novel bright and kink similariton solutions of cubic-quintic nonlinear Schrödinger equation with distributed coefficients

“…Moreover, the frequency shift and propagation trajectory of the similaritons are influenced by the system parameters M , 1 M , 2 l , 1 l 2 and l 3 shown in the equations (27c) and (27d). Here, we take the bright similariton I (20) and kink similariton (22) as examples to present the influence of these system parameters on the evolution characteristics of the similaritons in detail.…”

“…Figure 3 show the effects of the system parameters on the propagation characteristics of bright similariton I (20) and kink similariton (22) in the absent of gain/loss. Figures 3(a) and (b) depict the evolution of the similaritons when the linear external potential is absent and the dispersion parameter is constant.…”

“…Here e = 1 in similariton solutions (20)- (22). It is worth noting that the corresponding constraint condition can be obtained by equations (5), (14b) and (14c)…”

“…Dai et al [21] discussed the interaction and control of the bright and dark similariton pairs in the periodic distributed amplification system for the cubic nonlinear Schrödinger equation with harmonic external potential. For the variable coefficient cubic-quintic nonlinear Schrödinger equation with Raman effect and harmonic external potential, Yang et al [22] obtained the exact bright and dark 1-similariton and 2-similariton by means of the similarity transformation and the Hirota bilinear transformation methods, and revealed the transmission characteristics and tunneling behaviors of 2-similariton. Recently, the nonautonomous bright rogue wave solutions and the symmetric cnoidal wave solutions of the nonlinear Schrödinger equation including group velocity dispersion, cubic nonlinearity, external potential and gain/loss effects were presented by hidden symmetry reduction method in [23], and the propagation characteristics of the rogue wave and symmetric cnoidal wave solutions in the periodic distribution system and exponential distribution system were investigated.…”

Generation and controlling of ultrashort self-similar solitons and rogue waves in inhomogeneous optical waveguide

“…Over the past years, the concept of self-similarity has propelled the development of ultrafast nonlinear optics [18], specifically in the field of ultrashort self-similar pulse propagation [19,20] and ultrafast fiber lasers based on self-similar pulse evolution [21]. The ultrashort optical pulses can be realized by incorporating the higher-order effects such as third-order dispersion, self-steepening, self-frequency shift to the standard nonlinear Schrödinger equation known as higher order nonlinear Schrödinger equation (HNLSE) [22].…”