Soliton interaction for a variable-coefficient higher-order nonlinear Schrödinger equation in a dispersion-decreasing fiber

Huang, Zhi-Ruo; Wang, Yun-Po; Jia, Hongxia; Liu, Yingfang

doi:10.1016/j.optlastec.2018.01.026

Cited by 6 publications

(2 citation statements)

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“…However, the soliton transmission process can be simulated more accurately with the variable coefficient NLS (vcNLS) equation, when the transmission medium or boundary condition is not uniform [33], [34], [35], [36], [37], [38], [39], [40]. For the vcNLS equation, dynamics of solitons have been explored [33], and soliton interactions have been discussed [34], [35]. In addition, the breather-to-soliton transitions for the vcNLS equation have been found [36], and nonautonomous multipeak solitons have been obtained [37].…”

Section: Introductionmentioning

confidence: 99%

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Zhou

Mirzazadeh

et al. 2019

Journal of Advanced Research

128

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Section: Introductionmentioning

confidence: 99%

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Zhou

Mirzazadeh

et al. 2019

Journal of Advanced Research

128

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“…Via symbolic computation and Hirota method, bilinear forms, dark one-and two-soliton solutions and analytic soliton solutions for equation (1) are obtained [6][7][8]. Compared with the existing literatures, the Weierstrass elliptic function solutions obtained by using the auxiliary equation method have a broader inclusion.…”

Section: Introductionmentioning

confidence: 99%

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

Fan,

Bao

2023

Phys. Scr.

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In this paper, the auxiliary equation method is used to study the Weierstrass elliptic function solutions and degenerate solutions of the variable coefficient higher order Schrödinger equation, including Jacobian elliptic function solutions, trigonometric function solutions and hyperbolic function solutions. The types of solutions of the variable coefficient higher-order Schrödinger equation are enriched, and the method of seeking precise and accurate solutions is extended. It is concluded that the types of degenerate solutions are related to the coefficients of the equation itself when the degenerate solutions are obtained from the solutions of the Weierstrass elliptic functions. In addition, the solutions form of the equation is extended from the power series expansion form to the Laurent series expansion form, and the corresponding solutions are obtained. After the conversion formula between the Weierstrass elliptic function solutions and the Jacobian elliptic function solutions is constructed, the Jacobian elliptic function solutions of the higher order Schrödinger equation with variable coefficients are also obtained. These have not been previously studied.

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Dark soliton solutions for a variable coefficient higher-order Schrödinger equation in the dispersion decreasing fibers

Zhao

2022

Applied Mathematics Letters

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Soliton interaction for a variable-coefficient higher-order nonlinear Schrödinger equation in a dispersion-decreasing fiber

Cited by 6 publications

References 46 publications

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

Dark soliton solutions for a variable coefficient higher-order Schrödinger equation in the dispersion decreasing fibers

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