Advanced Studies in Pure Mathematics

Mathematical, numerical and experimental study of solitary waves

Jeongwhan Choi, Dal-Soo Lee, Sangho Oh, Shu-Ming Sun, and Sung-Im Whang

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Abstract

The note discusses the motion of solitary waves on the free surface of a layer of water. The rigorous results for the existence of solitary-wave solutions of exact governing equations are given. To generate such surface waves, a moving bump placed at the bottom or a pressure source on the free surface is used. A model equation, called forced Korteweg–de Vries (FKdV) equation, is numerically studied and multi- solitary- wave solutions are obtained. Then, the numerical solutions are compared with experimental results using a water tank with a moving bump at the bottom.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 263-271

Dates
Received: 29 March 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934222

Digital Object Identifier
doi:10.2969/aspm/06410263

Mathematical Reviews number (MathSciNet)
MR3381211

Zentralblatt MATH identifier
1335.76014

Subjects
Primary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76B25: Solitary waves [See also 35C11]

Keywords
Solitary waves forced KdV equations

Citation

Choi, Jeongwhan; Lee, Dal-Soo; Oh, Sangho; Sun, Shu-Ming; Whang, Sung-Im. Mathematical, numerical and experimental study of solitary waves. Nonlinear Dynamics in Partial Differential Equations, 263--271, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410263. https://projecteuclid.org/euclid.aspm/1540934222


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