Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a (3+1)-dimensional burgers system in ocean physics and hydrodynamics

IF 13 1区 工程技术 Q1 ENGINEERING, MARINE
Sachin Kumar , Amit Kumar , Brij Mohan
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引用次数: 18

Abstract

In the fields of oceanography, hydrodynamics, and marine engineering, many mathematicians and physicists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenomena, one of which is a (3+1)-dimensional Burgers system that is currently being studied. In this paper, we apply two different analytical methods, namely the generalized Kudryashov (GK) method, and the generalized exponential rational function method, to derive abundant novel analytic exact solitary wave solutions, including multi-wave solitons, multi-wave peakon solitons, kink-wave profiles, stripe solitons, wave-wave interaction profiles, and periodic oscillating wave profiles for a (3+1)-dimensional Burgers system with the assistance of symbolic computation. By employing the generalized Kudryashov method, we obtain some new families of exact solitary wave solutions for the Burgers system. Further, we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions, exponential rational function solutions, periodic breather-wave soliton solutions, dark and bright solitons, singular periodic oscillating wave soliton solutions, and complex multi-wave solutions under various family cases. Based on soft computing via Wolfram Mathematica, all the newly established solutions are verified by back substituting them into the considered Burgers system. Eventually, the dynamical behaviors of some established results are exhibited graphically through three - and two-dimensional wave profiles via numerical simulation.

海洋物理和流体动力学中(3+1)维Burgers系统的孤立波剖面演化动力学和丰富的解析解
在海洋学、流体力学和海洋工程领域,许多数学家和物理学家对Burgers型方程感兴趣,这些方程可以显示非线性波动现象的不同动力学,其中一个是目前正在研究的(3+1)维Burgers系统。在本文中,我们应用两种不同的分析方法,即广义Kudryashov(GK)方法和广义指数有理函数方法,导出了大量新的解析精确孤立波解,包括多波孤子、多波峰值孤子、扭结波轮廓、条纹孤子、波-波相互作用轮廓,在符号计算的辅助下,给出了(3+1)维Burgers系统的周期振荡波形。利用广义Kudryashov方法,我们得到了Burgers系统的一些新的精确孤立波解族。此外,我们应用广义指数有理函数方法获得了大量的孤立子解,形式为三角函数和双曲函数解、指数有理函数解、周期呼吸波孤立子解、暗孤子和亮孤子、奇异周期振荡波孤立子解决方案,以及各种族情况下的复杂多波解。基于Wolfram Mathematica的软计算,通过将所有新建立的解反代入所考虑的Burgers系统来验证它们。最后,通过数值模拟,通过三维和二维波浪剖面以图形方式展示了一些已建立结果的动力学行为。
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来源期刊
CiteScore
11.50
自引率
19.70%
发文量
224
审稿时长
29 days
期刊介绍: The Journal of Ocean Engineering and Science (JOES) serves as a platform for disseminating original research and advancements in the realm of ocean engineering and science. JOES encourages the submission of papers covering various aspects of ocean engineering and science.
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