This article presents soliton solutions to a generalized nonlinear Fokas-Lenells equation via the Sine-Gordon expansion method. To uncover the clear picture of the gained solutions, the two and three-dimensional figures for the solutions are given. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.

New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method

A new strategy exploiting together the modified Riemann–Liouville fractional derivative rule and two kinds of fractional dual-function methods with the Mittag–Leffler function is presented to solve fractional nonlinear models. As an example, the space-time fractional Fokas-Lenells equation is solved by this strategy, some new exact analytical solutions including bright soliton, dark soliton, combined soliton and periodic solutions are found. The comparison of two kinds of fractional dual-function methods is also presented. These solutions exist under a constraint among parameters of nonlinear dispersion, nonlinearity and self-steepening perturbation. In order to further study the optical soliton transport and better understand the physical phenomenon behind the model, dynamical characteristics of analytical fractional soliton solutions including some graphics and analysis is provided. The role of the fractional-order parameter is studied.

Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas-Lenells equation

https://iopscience.iop.org/article/10.1088/1572-9494/ab7ec8/pdf

Modulation instability analysis, optical and other solutions to the modified nonlinear Schrödinger equation

The (2+1)-dimensional generalized coupled nonlinear Schrodinger equation with the four-wave mixing (FWM) term is studied in this paper, which describes the optical solitons in a birefringent fiber. By virtue of the Hirota method, the one- and two-soliton solutions are derived. On the basis of solutions obtained, we discuss how the values of the FWM and some free parameters affect the solitons’ peformance. The FWM parameter can help to control the amplitude of the solitons. Meanwhile, by setting the values of certain free parameters, we can control the solitons’ propagation direction and speed, and reduce the interactions between them as well. In addition, the energy transfer of solitons during elastic collision and separation is also discussed. The conclusions here may be useful in improving the communication quality in multi-mode fibers.

Bright soliton solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing term

Research on the interactions between optical solitons is of great significance for the large capacity and long distance transmission in optical fibers. In this paper, interactions between periodic solitons are investigated for the first time. Analytic solution for the high-order nonlinear Schrodinger equation, which can be used to describe the periodic soliton transmission, is obtained based on the bilinear method. Interaction characteristics between periodic solitons are discussed. Influences of corresponding dispersion and nonlinear effects on their interactions are analyzed. Results provide theoretical guidance for the stable transmission of periodic solitons in inhomogeneous optical fibers.

Periodic soliton interactions for higher-order nonlinear Schrödinger equation in optical fibers

Phase-shift controlling can attenuate the interactions between solitons and gives practical advantage in optical communication systems. For the variable-coefficient nonlinear Schrodinger equation, which can be imitated the transmission of solitons in the dispersion-decreasing fiber, analytic three solitons solutions are derived via the Hirota method. Based on the obtained solutions, influences of the second-order dispersion parameters and other related parameters in different function types on the soliton transmission are discussed. Results declare that phase-shift controlling of solitons in dispersion-decreasing fiber can be achieved when the dispersion function is Gaussian one. In addition, by adjusting the constraint value, propagation distance of solitons can be further extended. This may be useful in the optical logic devices and ultra-short pulse lasers.

Phase-shift controlling of three solitons in dispersion-decreasing fibers

A fifth-order variable coefficient nonlinear Schrodinger equation based on original inhomogeneous model is proposed and studied. Bright multi-soliton analytic solutions of the equation are calculated through the Hirota method and auxiliary function. The effect of different constraints between fifth-order dispersion with third-order dispersion on soliton transmission is researched. Besides, their propagation and interaction dynamics are analyzed. Moreover, based on the obtained three-soliton solutions, we change the value of $$\beta (x)$$ to discuss the soliton propagation. Three different propagation and interaction structures are derived via adjusting the nonlinear term. The results can enrich the inhomogeneous model and apply in nonlinear optical fiber.

Suzhi Liu

Papers

Phase-shift controlling of three solitons in dispersion-decreasing fibers

Interactions among solitons for a fifth-order variable coefficient nonlinear Schrödinger equation