A study of the pulse propagation with a generalized Kudryashov equation

Hu, Xiang; Yin, Zhixiang

doi:10.1016/j.chaos.2022.112379

Cited by 16 publications

(3 citation statements)

References 26 publications

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“…Example 6. The generalized nonlinear Schrödinger equation with nonlinearities [37][38][39][40][41][42] i…”

Section: Hamiltonian Of the Generalized Nonlinear Schrödinger Equatio...mentioning

confidence: 99%

Hamiltonians of the Generalized Nonlinear Schrödinger Equations

Kudryashov

2023

Mathematics

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Some types of the generalized nonlinear Schrödinger equation of the second, fourth and sixth order are considered. The Cauchy problem for equations in the general case cannot be solved by the inverse scattering transform. The main objective of this paper is to find the conservation laws of the equations using their transformations. The algorithmic method for finding Hamiltonians of some equations is presented. This approach allows us to look for Hamiltonians without the derivative operator and it can be applied with the aid of programmes of symbolic calculations. The Hamiltonians of three types of the generalized nonlinear Schrödinger equation are found. Examples of Hamiltonians for some equations are presented.

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“…Example 6. The generalized nonlinear Schrödinger equation with nonlinearities [37][38][39][40][41][42] i…”

Section: Hamiltonian Of the Generalized Nonlinear Schrödinger Equatio...mentioning

confidence: 99%

Hamiltonians of the Generalized Nonlinear Schrödinger Equations

Kudryashov

2023

Mathematics

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“…where A j , (j = 0, 2, 4, 6) are constants to be determined. Equation (34) admits solutions having the form…”

Section: Mathematical Analysis Of Governing Modelmentioning

confidence: 99%

“…Different soliton structures were derived such as bright, dark, singular, bright-dark, singular-dark solitons and others. For more details about obtained results, reader is referred to the references [29][30][31][32][33][34][35][36]. The governing KE is given by…”

Section: Introductionmentioning

confidence: 99%

Chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity

Al-Ghafri,

Sankar,

Krishnan

et al. 2023

J. Eur. Opt. Society-Rapid Publ.

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The present study is devoted to investigate the chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity. Thus, the mathematical model consists of coupled nonlinear Schrödinger equation (NLSE) that describes pulse propagation in a medium of fiber Bragg gratings (BGs). To reach an integrable form for this intricate model, the phase-matching condition is applied to derive equivalent equations that are handled analytically. By means of auxiliary equation method which possesses Jacobi elliptic function (JEF) solutions, various forms of soliton solutions are extracted when the modulus of JEF approaches 1. The generated chirped gap solitons have different types of structures such as bright, dark, singular, W-shaped, kink, anti-kink and Kink-dark solitons. Further to this, two soliton waves namely chirped bright quasi-soliton and chirped dark quasi-soliton are also created. The dynamic behaviors of chirped gap solitons are illustrated in addition to their corresponding chirp. It is noticed that self-phase modulation and dispersive reflectivity have remarkable influences on the pulse propagation. These detailed results may enhance the engineering applications related to the field of fiber BGs.

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Wave structures and the chaotic behaviors of the cubic-quartic nonlinear Schrödinger equation for parabolic law in birefringent fibers

Kai

2023

Nonlinear Dyn

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A study of the pulse propagation with a generalized Kudryashov equation

Cited by 16 publications

References 26 publications

Hamiltonians of the Generalized Nonlinear Schrödinger Equations

Hamiltonians of the Generalized Nonlinear Schrödinger Equations

Chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity

Wave structures and the chaotic behaviors of the cubic-quartic nonlinear Schrödinger equation for parabolic law in birefringent fibers

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