大深度双层流体中界面孤子的衍射与相互作用

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Lei Hu, Xu-Dan Luo, Zhan Wang
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引用次数: 0

摘要

SIAM 应用数学杂志》,第 84 卷第 4 期,第 1385-1412 页,2024 年 8 月。 摘要本文旨在提出一个新颖的各向同性双向模型,用于研究由两个叠加的不可压缩不粘性流体组成的三维系统中的弱色散和弱非线性大气内波。新开发的方程是本杰明-本尼-卢克(BBL)方程,它是著名的二维本杰明-奥诺(2DBO)方程和本尼-卢克方程的一般化,利用水波的非局部阿布罗维茨-福卡斯-穆斯利马尼公式推导而来。通过采用经典的四阶 Runge-Kutta 方法、带积分因子方法的伪谱方案和窗口方案,BBL 和 2DBO 方程的演化结果表明,各向异性的 2DBO 方程与各向同性的 BBL 模型在所研究的问题上非常吻合,即焦点是孤子演化/相互作用区的中心部分。通过应用惠瑟姆调制理论,本文得到了二维BO方程的调制方程,用于分析五种不同初值问题(截断线孤子、线孤子、弯曲干孤子、弯曲孤子和反向弯曲孤子)中的孤子动力学。此外,还获得了相应的数值结果,结果表明与理论预测十分吻合。理论和数值结果都揭示了马赫膨胀的形成条件,以及马赫干振幅与初始数据之间的具体关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Diffraction and Interaction of Interfacial Solitons in a Two-Layer Fluid of Great Depth
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1385-1412, August 2024.
Abstract. This paper aims to present a novel isotropic bidirectional model for studying weakly dispersive and weakly nonlinear atmospheric internal waves in a three-dimensional system consisting of two superimposed, incompressible, and inviscid fluids. The newly developed equation is the Benjamin–Benney–Luke (BBL) equation, a generalization of the famous two-dimensional Benjamin–Ono (2DBO) equation and the Benney–Luke equation, derived using the nonlocal Ablowitz–Fokas–Musslimani formulation of water waves. The evolution results of the BBL and 2DBO equations, performed by implementing the classic fourth-order Runge–Kutta method, the pseudospectral scheme with the integrating factor method, and the windowing scheme, show that the anisotropic 2DBO equation agrees well with the isotropic BBL model for problems being investigated, namely the focus is the central part of the soliton evolution/interaction zone. By applying the Whitham modulation theory, modulation equations for the 2DBO equation are obtained in this paper for analyzing the soliton dynamics in five different initial-value problems (truncated line soliton, line soliton, bent-stem soliton, bent soliton, and reverse bent soliton). In addition, corresponding numerical results are obtained and shown to agree well with the theoretical predictions. Both theoretical and numerical results reveal the formation conditions of the Mach expansion, as well as the specific relationship between the amplitude of the Mach stem and the initial data.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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