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Most of the results in this paper rest upon the investi gation of properties of M. Formulas for the first and second variations of M will be derived. The functional M and its first variation 6m will be important in showing the impossibility of the existence of certain asymmetric periodic waves. In the special case in which the wave is almost flat, we indicate in Chapter 4 how M might be used to set up an existence proof for periodic waves on an ocean of infinite depth. In particular we show that for a fixed area and a certain fixed potential energy.
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A Variational Principle for Periodic Waves of Infinite Depth (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book investigates periodic waves on an ocean of infinite depth. The author constructs a functional and variational principle for these waves. They then prove the existence of asymmetric periodic waves and establish conditions for the existence of those waves with minimum kinetic energy. The author also derives a second variational formula for waves of small amplitude, showing it to be strictly positive when the area and potential energy are held fixed. This implies the wave minimizes the kinetic energy in this case. The author's results contribute to the study of existence and uniqueness of surface waves using variational methods. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332208999_0
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