Novel solitary wave and periodic solutions for the nonlinear Kaup–Newell equation in optical fibers

Wang, Kang-Le

doi:10.1007/s11082-023-06122-8

Cited by 7 publications

(1 citation statement)

References 55 publications

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“…Third-and higher-order equations from this hierarchy have not received as much attention as the second-order equation, which is the first equation of the hierarchy (for papers on that equation, see, for example, refs. [1][2][3][4][5][6][7]). In [8], a model for an integrable system of long lattice waves was derived, which is now known as the second equation of the Kaup-Newell hierarchy (1).…”

Section: Introductionmentioning

confidence: 99%

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

Kudryashov,

Lavrova

2024

Mathematics

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The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium.

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Section: Introductionmentioning

confidence: 99%

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

Kudryashov,

Lavrova

2024

Mathematics

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New mathematical approaches to nonlinear coupled Davey–Stewartson Fokas system arising in optical fibers

Wang

2024

Math Methods in App Sciences

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This research focuses on the nonlinear coupled Davey–Stewartson Fokas system, which models pulse propagation in monomode optical fibers. In order to find the novel periodic and solitary wave solutions of the nonlinear coupled Davey–Stewartson Fokas system, we have employed two effective mathematical techniques named as the Sine‐Gordon expansion method and the simple equation method. We found after researching into previous literature that these novel solutions are unique and have never been reported. Some 3D and 2D graphs are also used to discuss the dynamical behavior of these new solutions.

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Soliton Solutions of Nonlinear Geophysical Kdv Equation Via Two Analytical Methods

Behera,

Aljahdaly

2024

Int J Theor Phys

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Novel solitary wave and periodic solutions for the nonlinear Kaup–Newell equation in optical fibers

Cited by 7 publications

References 55 publications

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

New mathematical approaches to nonlinear coupled Davey–Stewartson Fokas system arising in optical fibers

Soliton Solutions of Nonlinear Geophysical Kdv Equation Via Two Analytical Methods

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