Please use this identifier to cite or link to this item: http://ithesis-ir.su.ac.th/dspace/handle/123456789/2771
Title: The existence of solution to wave equations on Legendrian curves
การมีอยู่ของผลเฉลยของสมการคลื่นบนเส้นโค้งเลอฌองเดรียน
Authors: Pitchaporn PAITONG
พิชชาพร ไผ่ทอง
Supap Kirtsaeng
สุภาพ เกิดแสง
Silpakorn University. Science
Keywords: Legendrian curve
contact manifold
standard contact structure
wave on a string
D'Alembert's Formula
general solution to wave equation
Issue Date:  18
Publisher: Silpakorn University
Abstract: The wave on a string has basically been studied in such a way that the movement of the string is in two dimensions and the solution to wave equation is obtained by D’Alembert’s Formula.  This work focuses on a wave on a curve of a string where the Legendrian base curve is a straight line x-axis. The ambient space of the curve is three dimensional space together with the standard contact structure. The Legendrian condition and the initial conditions of the vector wave equation on 1-manifold are the key to acquire the theorem which leads to the necessary conditions for the existence of nontrivial Legendrian wave.  The result turns out that fixed initial position on xz-plane, zero initial position along xy-plane, zero initial velocity on xy-plane and xz-plane including zero sum of the external force along y-axis  are the necessary conditions. An example of the existence of such wave has been given. The study brings the conclusion that there exists a Legendrian wave on the x-axis Legendrian base curve.
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Description: Master of Science (M.Sc.)
วิทยาศาสตรมหาบัณฑิต (วท.ม)
URI: http://ithesis-ir.su.ac.th/dspace/handle/123456789/2771
Appears in Collections:Science

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