Natural Vibrations of the Shallow Water Equation
R. D. Ortiz *
Faculty of Natural Sciences, University of Cartagena, Stone Head Bolivar Avenue Consulate, Cartagena de Indias, Bolivar, Colombia.
A. M. Marin
Faculty of Natural Sciences, University of Cartagena, Stone Head Bolivar Avenue Consulate, Cartagena de Indias, Bolivar, Colombia.
J. A. Rodriguez
Instituto Tecnologico de Morelia, Morelia, Mexico.
*Author to whom correspondence should be addressed.
Abstract
The purpose of this paper is to construct the asymptotic for natural frequencies of the shallow water problem using the method of Wentzel-Kramers-Brillouin (WKB) and find the secular equation for the eigenvalues.
Keywords: Shallow water equation, Asymptotics, Eigenfunctions, Eigenvalues, Water waves, WKB method