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A Note on the Analytical Resolution of a Nonhydrostatic Standing‐Wave Eigenvalue Problem for a Parabolic Basin
Author(s) -
Lundberg P.
Publication year - 1993
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19930731011
Subject(s) - eigenvalues and eigenvectors , series (stratigraphy) , power series , transformation (genetics) , mathematics , mathematical analysis , range (aeronautics) , resolution (logic) , simple (philosophy) , physics , geology , chemistry , materials science , quantum mechanics , philosophy , epistemology , artificial intelligence , computer science , composite material , paleontology , biochemistry , gene
The eigenvalue problem determining the periods of slightly nonhydrostatic standing waves in a basin with parabolic bottom profile has previously been resolved using Frobenius series representations of the solutions in conjunction with boundedness conditions at the basin endpoints. Here it is shown that by subjecting the governing equation to a Benjamin‐Bona‐Mahony transformation the problem is considerably simplified and that the range of validity of a simple power series solution exceeds the one previously obtained.