A NOTE ON THE ANALYTICAL RESOLUTION OF A NONHYDROSTATIC STANDING-WAVE EIGENVALUE PROBLEM FOR A PARABOLIC BASIN

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