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

Demiray, Şeyma Tülüce; BAYRAKCI, Uğur

doi:10.21597/jist.861864

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…The purpose of this article is to detect soliton solutions of strain wave equation and (2+1)-dimensional BK equation using GKM [24][25][26][27]. First of all, the features of GKM, which is the method we used in our study, are explained.…”

Section: Introductionmentioning

confidence: 99%

Application of the GKM of to some nonlinear partial equations

TÜLÜCE DEMİRAY,

BAYRAKCI,

YILDIRIM

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this manuscript, the strain wave equation, which plays an important role in describing different types of wave propagation in microstructured solids and the (2+1) dimensional Bogoyavlensky Konopelchenko equation, is defined in fluid mechanics as the interaction of a Riemann wave propagating along the $y$-axis and a long wave propagating along the $x$-axis, were studied. The generalized Kudryashov method (GKM), which is one of the solution methods of partial differential equations, was applied to these equations for the first time. Thus, a series of solutions of these equations were obtained. These found solutions were compared with other solutions. It was seen that these solutions were not shown before and were presented for the first time in this study. The new solutions of these equations might have been useful in understanding the phenomena in which waves are governed by these equations. In addition, 2D and 3D graphs of these solutions were constructed by assigning certain values and ranges to them.

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Section: Introductionmentioning

confidence: 99%

Application of the GKM of to some nonlinear partial equations

TÜLÜCE DEMİRAY,

BAYRAKCI,

YILDIRIM

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Different analytical approaches for finding novel optical solitons with generalized third-order nonlinear Schrödinger equation

et al. 2021

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New Solutions for IOPM and (3+1)-Dimensional NLWE in Liquid with Gas Bubbles

Demiray

CEREN>

2022

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Generalized Kudryashov method (GKM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been used to obtain some solutions of Ivancevic option pricing model (IOPM) and (3+1)-dimensional nonlinear wave equation (NLWE) in liquid with gas bubbles. Thus, some solutions of the discussed equations have been found such as dark soliton, trigonometric and hyperbolic solutions. Two dimensional (2D) and three dimensional (3D) graphics of these solutions have been drawn with the help of Wolfram Mathematica 12.

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

Cited by 6 publications

References 22 publications

Application of the GKM of to some nonlinear partial equations

Application of the GKM of to some nonlinear partial equations

Different analytical approaches for finding novel optical solitons with generalized third-order nonlinear Schrödinger equation

New Solutions for IOPM and (3+1)-Dimensional NLWE in Liquid with Gas Bubbles

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