New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation

Demiray, Şeyma Tülüce

doi:10.3390/e17096025

Cited by 44 publications

(12 citation statements)

References 42 publications

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“…In the view of such information, the solutions Eqs. (26), (28) and (30) of Eq. (1) are dark soliton solutions.…”

Section: Physical Explanationmentioning

confidence: 99%

New soliton solutions of the system of equations for the ion sound and Langmuir waves

Demiray

2016

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

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“…In the view of such information, the solutions Eqs. (26), (28) and (30) of Eq. (1) are dark soliton solutions.…”

Section: Physical Explanationmentioning

confidence: 99%

New soliton solutions of the system of equations for the ion sound and Langmuir waves

Demiray

2016

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Our aim in this article is ascertain the soliton solutions of generalized third-order (NLSE) through GKM (Tuluce Demiray and Bulut, 2015;Pandir et al, 2016;Tuluce Demiray and Bulut, 2016;Tuluce Demiray and Bulut, 2017;Tuluce Demiray and Bulut, 2019). In Section 2, GKM's basic structure is given.…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

Demiray¹,

BAYRAKCI²

2021

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, we have worked on GKM in order to obtain the soliton solutions of the generalized third-order nonlinear Schrödinger equation. Thus, we have acquired some new soliton solutions of the generalized third-order nonlinear Schrödinger equation which has an important usage area in optical fiber. Also, we have drawn some 2D and 3D surfaces of these obtained results by using Wolfram Mathematica 12. Then, we have shown the validity of the obtained solutions.

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“…The structure of many special solitary waves of the partial differential equation (PDE) is explained in terms of solitons (see previous studies). Solitary wave solutions also appear on propagating systems that are characterized by nonlinearity and dissipation.…”

Section: Introductionmentioning

confidence: 99%

Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity

Srivástava

Günerhan

Ghanbari

2019

Math Methods in App Sciences

112

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The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink-type, bright, dark, and singular soliton solutions are reported, and several numerical simulations are also included. The calculations are carried out by Maple software. All of the solutions that are derived in this paper are believed to be new and have presumably not been reported in earlier publications.

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New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation

Cited by 44 publications

References 42 publications

New soliton solutions of the system of equations for the ion sound and Langmuir waves

New soliton solutions of the system of equations for the ion sound and Langmuir waves

Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity

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