分数耦合非线性赫尔姆霍兹方程的新计算方法

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
KangLe Wang
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引用次数: 0

摘要

目的本文的主要目的是通过两种新的分析方法研究分数耦合非线性亥姆霍兹方程。设计/方法/途径本文利用保角导数对分数耦合非线性亥姆霍兹方程进行了初步研究。文章采用分数法和分数简单方程法等方法,成功地找到了新的分数周期解和孤波解。然后,这些分数周期解和孤波解的动力学以适当参数和分形维数的三维图形表示。这项研究有助于更深入地理解和详细探索高维孤波传播所涉及的动力学问题。研究结果所提出的两种数学方法可以简单高效地求解分数演化方程。所得到的分数周期解和孤波解都是全新的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New computational approaches to the fractional coupled nonlinear Helmholtz equation

Purpose

The main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.

Design/methodology/approach

This article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.

Findings

The proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.

Originality/value

The fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.

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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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