Optical soliton shaping in dispersion decreasing fibers

Liu, Wenjun; Pang, Lihui; Yan, Hao; Lei, Ming

doi:10.1007/s11071-016-2639-y

Cited by 46 publications

(3 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

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

Fan,

Bao

2023

Phys. Scr.

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

“…a 0 = 2, a 1 = 1, according to the solutions(7), we get According to the conversion formula (68) and θ = c 2 , we get the generalized Jacobian elliptic function solutions of equation(1) …”

mentioning

confidence: 99%

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

Fan,

Bao

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…[6−9] The effects of variable coefficients and external potentials on the solutions of the higher-order NLSE have been studied by Refs. [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Lax Pairs and Integrability Conditions of Higher-Order Nonlinear Schrödinger Equations

Asaduzzaman

Samet

Khawaja

2016

Commun. Theor. Phys.

View full text Add to dashboard Cite

We derive the Lax pairs and integrability conditions of the nonlinear Schrödinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrödinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrödinger equation.

show abstract