New extended generalized Kudryashov method for solving three nonlinear partial differential equations

Zayed, Elsayed M.E.; Shohib, Reham M.A.

doi:10.15388/namc.2020.25.17203

Cited by 12 publications

(13 citation statements)

References 39 publications

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“…To obtain the optical traveling wave solutions for the Hirota-Maccari system, we substitute Equations ( 9)- (15) into Equation (23) to obtain the following five optical traveling wave solutions:…”

Section: Applicationmentioning

confidence: 99%

“…One of the popular examples of such methods is the Kudryashov method, which typically only performs the calculation without the need for the form of a specific function. Examples of Kudryashov methods include the extended Kudryashov method [21], the generalized Kudryashov method [22], and the new extended generalized Kudryashov method [23]. The generalized Kudryashov method by Kaplan et al [22] does usefully apply to the nonlinear Jaulent-Miodek hierarchy and (2 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff equation.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we construct the exact significant solutions for different types of cases of the exp(−ϕ(ζ))-expansion method and AKM. Both methods are used as powerful mathematical tools for constructing traveling wave solutions of nonlinear partial differential equations (see, for example, [20][21][22][23][24][25][26]).…”

Section: Introductionmentioning

confidence: 99%

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Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Alotaibi

2021

Symmetry

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The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hirota–Maccari equation by using two different methods: the exp(−φ(ζ)) expansion method and Addendum to Kudryashov’s method to obtain the optical traveling wave solutions. By utilizing suitable transformations, the nonlinear pdes are transformed into odes. The traveling wave solutions are expressed in terms of rational functions. For certain parameter values, the obtained optical solutions are described graphically with the aid of Maple 15 software.

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Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Alotaibi

2021

Symmetry

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“…This saves the computational overhead and storage overhead associated with grid dissection. The computational principle is as follows [6]:…”

Section: Partial Differential Equations Based On Imagementioning

confidence: 99%

A Partial Differential Equation-Based Image Restoration Method in Environmental Art Design

2021

Advances in Mathematical Physics

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With the rapid development of networks and the emergence of various devices, images have become the main form of information transmission in real life. Image restoration, as an important branch of image processing, can be applied to real-life situations such as pixel loss in image transmission or network prone to packet loss. However, existing image restoration algorithms have disadvantages such as fuzzy restoration effect and slow speed; to solve such problems, this paper adopts a dual discriminator model based on generative adversarial networks, which effectively improves the restoration accuracy by adding local discriminators to track the information of local missing regions of images. However, the model is not optimistic in generating reasonable semantic information, and for this reason, a partial differential equation-based image restoration model is proposed. A classifier and a feature extraction network are added to the dual discriminator model to provide category, style, and content loss constraints to the generative network, respectively. To address the training instability problem of discriminator design, spectral normalization is introduced to the discriminator design. Extensive experiments are conducted on a data dataset of partial differential equations, and the results show that the partial differential equation-based image restoration model provides significant improvements in image restoration over previous methods and that image restoration techniques are exceptionally important in the application of environmental art design.

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“…Hence, familiarity with all classic and recently established approaches for addressing these models becomes increasingly vital. Over the past few years, numerous strategies have been proposed by mathematicians and scientists, such as the F-expansion method [8], the variational iteration method [9], method of sine-cosine [10], the tanh-function technique [11], the auxiliary equation method [12], the exp-function technique [13,14], the exact soliton solution [15][16][17], the generalized Kudryashov approach [18], and the newly extended generalized Kudryashov approach [19]. A more detailed discussion on some recent direct methods can be found in several related works (see, for example, [20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches

Alotaibi

2022

Crystals

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The study of nonlinear evolution equations is a subject of active interest in different fields including physics, chemistry, and engineering. The exact solutions to nonlinear evolution equations provide insightful details and physical descriptions into many problems of interest that govern the real world. The Kadomtsev–Petviashvili (kp) equation, which has been widely used as a model to describe the nonlinear wave and the dynamics of soliton in the field of plasma physics and fluid dynamics, is discussed in this article in order to obtain solitary solutions and explore their physical properties. We obtain several new optical traveling wave solutions in the form of trigonometric, hyperbolic, and rational functions using two separate direct methods: the (w/g)-expansion approach and the Addendum to Kudryashov method (akm). The nonlinear partial differential equation (nlpde) is reduced into an ordinary differential equation (ode) via a wave transformation. The derived optical solutions are graphically illustrated using Maple 15 software for specific parameter values. The traveling wave solutions discovered in this work can be viewed as an example of solutions that can empower us with great flexibility in the systematic analysis and explanation of complex phenomena that arise in a variety of problems, including protein chemistry, fluid mechanics, plasma physics, optical fibers, and shallow water wave propagation.

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New extended generalized Kudryashov method for solving three nonlinear partial differential equations

Cited by 12 publications

References 39 publications

Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

A Partial Differential Equation-Based Image Restoration Method in Environmental Art Design

Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches

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