Exploring soliton dynamics and wave interactions in an extended Kadomtsev-Petviashvili-Boussinesq equation

IF 5.9 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Ain Shams Engineering Journal Pub Date : 2025-07-01 Epub Date: 2025-04-15 DOI:10.1016/j.asej.2025.103395

Nauman Raza , Adil Jhangeer , Zeeshan Amjad , Beenish Rani , Dumitru Baleanu

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Abstract

This research investigates the extended Kadomtsev-Petviashvili-Boussinesq equation, relevant in numerous scenarios involving dissipative media. To initiate the analysis, a Hirota bilinear form is applied, leading to a Bäcklund transformation for the equation. Utilizing this bilinear Bäcklund transformation, we derive solutions comprising rational and exponential functions. Moreover, the Hirota bilinear representation is employed extensively to decipher the dynamics of two-wave, three-wave, rogue, lump-kink, breather, and multi-wave solutions. Detailed visualizations, including contour plots and 3D profiles across diverse parameter settings, offer deeper insights into the characteristics of these results. A traveling wave transformation further simplifies the equation into an ordinary differential equation, and the use of a new auxiliary equation method yields solutions that encompass trigonometric, hyperbolic, rational, and exponential functions. Our results highlight the effectiveness and efficiency of these methods in analytically solving nonlinear partial differential equations.

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扩展Kadomtsev-Petviashvili-Boussinesq方程中孤子动力学和波相互作用的探索

本研究探讨了扩展Kadomtsev-Petviashvili-Boussinesq方程，该方程与涉及耗散介质的许多场景相关。为了开始分析，应用了Hirota双线性形式，导致方程的Bäcklund变换。利用这个双线性Bäcklund变换，我们得到了包含有理函数和指数函数的解。此外，Hirota双线性表示被广泛用于解读两波、三波、流氓、块状扭结、呼吸和多波解的动力学。详细的可视化，包括不同参数设置的等高线图和3D轮廓，可以更深入地了解这些结果的特征。行波变换进一步将方程简化为常微分方程，并使用新的辅助方程方法得到包含三角函数、双曲函数、有理函数和指数函数的解。我们的结果突出了这些方法在解析求解非线性偏微分方程中的有效性和效率。

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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.