(2+1)-色散长波方程的相似解

IF 13 1区 工程技术 Q1 ENGINEERING, MARINE
Raj Kumar , Ravi Shankar Verma , Atul Kumar Tiwari
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引用次数: 6

摘要

本文致力于得到在恒定深度的无限长通道中传播的(2+1)耦合色散长波方程的一组新的解析解,这些方程可以在公海或宽通道中观测。利用相似变换方法的不变性,通过单参数李群理论得到了解。重复使用相似性转换方法可以将偏微分方程系统转换为常微分方程系统。在适当的限制条件下,解出了ODE的简化系统。数值模拟是为了以物理意义上的方式描述解。通过适当选择其中涉及的函数和常数来模拟解的轮廓。在每个动画中,都会捕获一个用于支配行为的帧。它们表现出弹性多孤子、单孤子、双孤子、静止、扭结和抛物性质。这些结果是重要的,因为这些已经证实了S.Kumar等人。(2020)和K.Sharma等人。(2020)。他们的一些解可以从这项工作的结果中推导出来。现有文献中的其他结果与本工作中的结果不同。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On similarity solutions to (2+1)-dispersive long-wave equations

This work is devoted to get a new family of analytical solutions of the (2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth, and can be observed in an open sea or in wide channels. The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory. The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs. Under adequate restrictions, the reduced system of ODEs is solved. Numerical simulation is performed to describe the solutions in a physically meaningful way. The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein. In each animation, a frame for dominated behavior is captured. They exhibit elastic multisolitons, single soliton, doubly solitons, stationary, kink and parabolic nature. The results are significant since these have confirmed some of the established results of S. Kumar et al. (2020) and K. Sharma et al. (2020). Some of their solutions can be deduced from the results derived in this work. Other results in the existing literature are different from those in this work.

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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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