A Mathematical Analysis of a Model Involving an Integrable Equation for Wave Packet Envelope

Kaplan, Melike; Akbulut, Arzu

doi:10.1155/2022/3486780

Cited by 7 publications

(1 citation statement)

References 27 publications

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“…Te exact solutions of the nonlinear partial diferential equations (NLPDEs) have an important place in diferent felds of science, such as fuid mechanics, plasma physics, solid-state physics, and optical fbers. Tis being the case, many methods were discovered to solve nonlinear partial diferential equations, for example, the method of undetermined coefcients [1], the Riccati equation mapping approach [2], the trial equation method [3], the fnite element method [4], the extended trial approach [5], the Petrov-Galerkin method [6], the unifed and exp a function methods [7], the modifed extended tanh expansion method [8], the modifed simple procedure [9], the exponential rational function procedure [10], the Kudryashov method [11], the ansatz method [12], and so on.…”

Section: Introductionmentioning

confidence: 99%

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

Akbulut

2023

Journal of Mathematics

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The main idea of this study is to obtain the soliton-type solutions of the conformable time-fractional complex Ginzburg–Landau equation with Kerr law nonlinearity. For this aim, the generalized and modified Kudryashov methods are applied to the given model. The reason for using a conformable derivative is that the chain rule can be applied to this derivative. Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. According to our results, both of the used methods are effective and powerful. Finally, 3D and contour plots are given for some results with suitable variables. Our findings in this paper are critical for explaining a wide range of scientific and physical applications. According to our knowledge, our results are new in the literature.

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Section: Introductionmentioning

confidence: 99%

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

Akbulut

2023

Journal of Mathematics

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A Structural Approach to Gudermannian Functions

Gambini,

Nicoletti,

Ritelli

2023

Results Math

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The Gudermannian function relates the circular angle to the hyperbolic one when their cosines are reciprocal. Whereas both such angles are halved areas of circular and hyperbolic sectors, it is natural to develop similar considerations within the study of a class of curves images of maps with constant areal speed. After a brief exposition of some use of the Gudermannian in applied sciences, we proceed to illustrate the class of curves, called Keplerian curves, which can be parametrised by a map $${{\textbf{m}}}= (\cos _{{{\textbf{m}}}}, \sin _{{{\textbf{m}}}})$$ m = ( cos m , sin m ) whose areal speed is 1. In the next Sections, after a detailed study of p-circular and hyperbolic Fermat curves $$\mathscr {F}_p$$ F p and $$\mathscr {F}^*_p$$ F p ∗ , we define the p-Gudermannian as the primitive of the derivative of the p-hyperbolic sine divided by the square of the p-hyperbolic cosine: all the analogues of the classical identities are proven. Having realised that such curves correspond to each other by means a homology, we extend our study to a wide class of Keplerian curves and their homologues; once again, defined the Gudermannian in an identical manner, all the analogues of classical identities subsist. Below, three examples are detailed. The last paragraph further extends this consideration, eliminating the hypothesis that the curves are parametrised by maps with areal speed 1. The Appendix illustrates integrating techniques for systems defining the Fermat curves and determining the inverse of their tangent function.

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Solution of the non-linear time-fractional Kudryashov–Sinelshchikov equation using fractional reduced differential transform method

Tamboli,

Tandel

2024

Bol. Soc. Mat. Mex.

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A Mathematical Analysis of a Model Involving an Integrable Equation for Wave Packet Envelope

Cited by 7 publications

References 27 publications

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

A Structural Approach to Gudermannian Functions

Solution of the non-linear time-fractional Kudryashov–Sinelshchikov equation using fractional reduced differential transform method

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