Obtaining analytical solutions of (2+1)-dimensional nonlinear Zoomeron equation by using modified F-expansion and modified generalized Kudryashov methods

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Engineering Computations Pub Date : 2024-07-02 DOI:10.1108/ec-10-2023-0688
Muslum Ozisik, A. Secer, Mustafa Bayram
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Abstract

Purpose

The purpose of the article is to conduct a mathematical and theoretical analysis of soliton solutions for a specific nonlinear evolution equation known as the (2 + 1)-dimensional Zoomeron equation. Solitons are solitary wave solutions that maintain their shape and propagate without changing form in certain nonlinear wave equations. The Zoomeron equation appears to be a special model in this context and is associated with other types of solitons, such as Boomeron and Trappon solitons. In this work, the authors employ two mathematical methods, the modified F-expansion approach with the Riccati equation and the modified generalized Kudryashov’s methods, to derive various types of soliton solutions. These solutions include kink solitons, dark solitons, bright solitons, singular solitons, periodic singular solitons and rational solitons. The authors also present these solutions in different dimensions, including two-dimensional, three-dimensional and contour graphics, which can help visualize and understand the behavior of these solitons in the context of the Zoomeron equation. The primary goal of this article is to contribute to the understanding of soliton solutions in the context of the (2 + 1)-dimensional Zoomeron equation, and it serves as a mathematical and theoretical exploration of the properties and characteristics of these solitons in this specific nonlinear wave equation.

Design/methodology/approach

The article’s methodology involves applying specialized mathematical techniques to analyze and derive soliton solutions for the (2 + 1)-dimensional Zoomeron equation and then presenting these solutions graphically. The overall goal is to contribute to the understanding of soliton behavior in this specific nonlinear equation and potentially uncover new insights or applications of these soliton solutions.

Findings

As for the findings of the article, they can be summarized as follows: The article provides a systematic exploration of the (2 + 1)-dimensional Zoomeron equation and its soliton solutions, which include different types of solitons. The key findings of the article are likely to include the derivation of exact mathematical expressions that describe these solitons and the successful visualization of these solutions. These findings contribute to a better understanding of solitons in this specific nonlinear wave equation, potentially shedding light on their behavior and applications within the context of the Zoomeron equation.

Originality/value

The originality of this article is rooted in its exploration of soliton solutions within the (2 + 1)-dimensional Zoomeron equation, its application of specialized mathematical methods and its successful presentation of various soliton types through graphical representations. This research adds to the understanding of solitons in this specific nonlinear equation and potentially offers new insights and applications in this field.

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用修正的 F 展开法和修正的广义库德里亚肖夫法求得 (2+1) 维非线性佐默伦方程的解析解
目的 本文旨在对一个特定非线性演化方程(即 (2 + 1)-dimensional Zoomeron 方程)的孤子解进行数学和理论分析。孤子是在某些非线性波方程中保持形状和传播而不改变形式的孤波解。在这种情况下,佐默龙方程似乎是一个特殊的模型,并与其他类型的孤子(如 Boomeron 和 Trappon 孤子)相关联。在这项研究中,作者采用了两种数学方法,即里卡蒂方程的修正 F 展开方法和修正的广义库德里亚绍夫方法,推导出各种类型的孤子解。这些解包括扭结孤子、暗孤子、亮孤子、奇异孤子、周期奇异孤子和有理孤子。作者还从不同维度展示了这些解,包括二维、三维和等高线图形,这有助于直观地理解这些孤子在佐默伦方程中的行为。本文的主要目标是帮助人们理解 (2 + 1) 维佐默龙方程中的孤子解,并对这一特定非线性波方程中这些孤子的属性和特征进行数学和理论探索。设计/方法/途径本文的方法包括应用专门的数学技术分析和推导 (2 + 1) 维佐默龙方程的孤子解,然后以图形的方式展示这些解。总体目标是促进对这一特定非线性方程中孤子行为的理解,并有可能发现这些孤子解的新见解或应用:文章系统地探讨了 (2 + 1)-dimensional Zoomeron 方程及其孤子解,其中包括不同类型的孤子。文章的主要发现可能包括推导出描述这些孤子的精确数学表达式,以及这些解的成功可视化。这些发现有助于更好地理解这一特定非线性波方程中的孤子,有可能揭示它们在佐默龙方程中的行为和应用。原创性/价值这篇文章的原创性源于它对 (2 + 1) 维佐默龙方程中孤子解的探索、对专门数学方法的应用以及通过图形表示法对各种孤子类型的成功呈现。这项研究加深了人们对这一特定非线性方程中孤子的理解,并有可能为这一领域提供新的见解和应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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