Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

被引：3

作者：

Cheviakov, Alexei F. ^{[1
]}

机构：

[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK, Canada

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2018年 / 370卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Shallow water equations; Two-fluid model; Internal waves; Exact solutions; Solitary wave; Periodic wave; INTERNAL SOLITARY WAVES; GREEN-NAGHDI EQUATIONS; KORTEWEG-DE-VRIES; CONSERVATION-LAWS; DIFFERENTIAL-EQUATIONS; SHALLOW-WATER; SYSTEM; COMPUTATION; DERIVATION; DYNAMICS;

D O I：

10.1016/j.physd.2018.01.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：14 / 28

页数：15

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