Exploring multi-soliton patterns, bifurcation analysis, and chaos in (2+1) dimensions: A study on nonlinear dynamics

IF 6 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Ain Shams Engineering Journal Pub Date : 2024-06-29 DOI:10.1016/j.asej.2024.102917

Ziyad A. Alhussain

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引用次数: 0

Abstract

This study explores the intrinsic characteristics of the (2+1)-dimensional Schwarz-Korteweg-de Vries equation used to describe shallow water waves. The multiple solitons are successfully constructed using a technique involving multiple exponential functions. Graphical representations of the results are provided in 3D, 2D, and density plots to assess the compatibility of the solutions. Also, the dynamic nature of studied equation is examined based on bifurcation and chaos theory for nonlinear systems. Bifurcation signifies how our dynamical system is affected by physical parameters in planar dynamical system. After that, we apply the external force on planar dynamical system to show the chaotic like behavior of the studied model. Such behavior is confirmed by utilizing different chaos detecting tools. The obtained results serve to explain the effectiveness and applicability of the utilized methodologies in comprehend the exact solution and qualitative behavior of nonlinear physical models.

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探索 (2+1) 维的多孑子模式、分岔分析和混沌：非线性动力学研究

本研究探讨了用于描述浅水波的（2+1）维 Schwarz-Korteweg-de Vries 方程的内在特征。使用涉及多个指数函数的技术成功构建了多重孤子。研究结果以三维、二维和密度图的形式呈现，以评估解的兼容性。此外，还根据非线性系统的分岔和混沌理论研究了所研究方程的动态性质。分岔标志着我们的动力系统如何受到平面动力系统中物理参数的影响。然后，我们对平面动力系统施加外力，以显示所研究模型的混沌行为。我们利用不同的混沌检测工具证实了这种行为。所获得的结果有助于解释所使用的方法在理解非线性物理模型的精确解和定性行为方面的有效性和适用性。

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

Ain Shams Engineering Journal Engineering-General Engineering

CiteScore

10.80

自引率

13.30%

发文量

441

审稿时长

49 weeks

期刊介绍： in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance. Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.