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Research Article Open access CC BY 2.0

Natural Vibrations of the Shallow Water Equation

R. D. Ortiz, A. M. Marin, J. A. Rodriguez

Journal of Advances in Mathematics and Computer Science · pp. 649–654 · Published 12 Jul 2013

10.9734/BJMCS/2013/4465

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.

Shallow water equation Asymptotics Eigenfunctions Eigenvalues Water waves WKB method

References (6)

  1. 1 Water Wave Mechanics for Engineers and Scientists [DOI]
  2. 2 The applied dynamics of ocean surface waves [DOI]
  3. 3 Shock-Capturing Methods for Free-Surface Shallow Flows
  4. 4 Asymptotic Analysis : Linear Ordinary Differential Equations
  5. 5 High-Precision Methods in Eigenvalue Problems and Their Applications [DOI]
  6. 6 Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique [DOI]

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