Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation

Abstract

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

Discrete Bright-dark Soliton Interaction Dynamic Behaviors for Nonautonomous 2+1-Dimensional Soliton Equation

“…Yu presents the NDBSSs and their interactions of AL equation in Ref. [40]. Here, we further extend and investigate the 2+1-dimensional NDBDSSs and some dynamic behaviors, which is different from those results in the 1+1-dimensional work.…”

Some space-time fractional bright–dark solitons and propagation manipulations for a fractional Gross–Pitaevskii equation with an external potential

“…Some exact nonautonomous matterwave solutions (W-bright soliton, U-shaped dark soliton, periodic wave soliton, and rational soliton) are derived in [4]. Some nonautonomous discrete rogue wavesare reported in discrete soliton equations [5][6][7][8], and some nonautonomous discrete bright soliton solutions are considered in the generalized GP equation [9]. Especially, some GP equations with parity-time(PT)-symmetric potentials are studied via the inverse scattering transformation, then many physically relevant soliton solutions are obtained in [10][11][12][13][14].…”

Controllable optical superregular breathers in the femtosecond regime

“…Recently, the inhomogeneous fibers have aroused extensive attention to reflect the inhomogeneities of media, nonuniformities of boundaries, and external forces. [34][35][36][37][38][39][40] Furthermore, different types of femtosecond localized waves in the nonautonomous higher-order NLSE have been investigated, including solitons, [41][42][43][44] rogue waves, [45] breathers, [46] and so on. [47,48] In particular, the bright solitons in an exponential dispersion fiber and a periodic distributed fiber system have been observed experimentally.…”