Characteristics of nonautonomous W-shaped soliton and Peregrine comb in a variable-coefficient higher-order nonlinear Schrödinger equation

Zhang, Xing; Zhao, Yue; Qi, Feng-Hua; Cai, Liu-Ying

doi:10.1016/j.spmi.2016.10.072

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…To contribute to the studies of the higher order Schrödinger equation and the special cases of this equation in the literature [31,32,[45][46][47], we considered Equation (4). This equation was considered in [29,30] for α 2 = 1 2 and the authors studied the non autonomous characteristics of the W-shaped solitons and have modified the Darboux transformation method to find rational solutions of the equation of the first and second orders, respectively. As far as we know, the exact solutions of this equation, which include generalized hyperbolic and trigonometric functions, were investigated for the first time in this research.…”

Section: Resultsmentioning

confidence: 99%

“…Case (i) X 2 By solving the characteristic equation (29) for the generator X 2 , similarity variables are obtained as follows:…”

Section: Symmetry Reduction and Invariant Solutionsmentioning

confidence: 99%

“…This method has a finite series expansion form based on the balancing principle. Higher order NLSEs were taken into consideration by researchers in recent years [11,[29][30][31][32]. However, to the best of our knowledge, the exact solutions that contain generalized hyperbolic and trigonometric functions of third-order NLS equations have not been studied.…”

Section: Introductionmentioning

confidence: 99%

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A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Yaşar

Seadawy

2020

Journal of Taibah University for Science

120

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In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic, trigonometric and rational solutions that are more general than classical ones. Secondly, we construct the transformation groups which left the equations invariant and vector fields with the Lie symmetry groups approach. With the help of these vector fields, we obtain the symmetry reductions and exact solutions of the equation. The obtained groupinvariant solutions are Jacobi elliptic function and exponential type. We discuss the dynamic behaviour and structure of the exact solutions for distinct solutions of arbitrary constants. Lastly, we obtain conservation laws of the considered equation by construing the complex equation as a system of two real partial differential equations (PDEs).

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