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Degree

Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics, 2011.

Abstract

Across the country, school students learn that ocean waves cause water particles to form looping paths, traveling in circles which become smaller as you look deeper underwater.

In this paper, we investigate the approximations which are used to make this claim. Furthermore, we investigate closer approximation techniques which show that these looping paths actually propogate forward with the wave's motion. Finally, we investigate the specific case of the soliton, which causes particles underneath to travel in a forward-moving arc, with no looping motion at all.

With this background, we examine the recent work of A. Constantin and collaborators, specifically his conclusion that our results for the soliton hold for any solitary wave.

Subject Headings

Applied Mathematics; Fluid Dynamics; Mathematics; Physics

Keywords

Solitons; Fluid dynamics; Water waves; Euler equation; KdV equation; Differential equations

Committee / Advisors

George T. Yates, PhD (Advisor)
Jozsi Jalics, PhD (Committee Member)
Steven L. Kent, PhD (Committee Member)

Pages

ix, 83 p.

Document number: ysu1311100628
Permalink: http://rave.ohiolink.edu/etdc/view?acc_num=ysu1311100628

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