| Abstract: | The propagation of a pulse on the surface of a liquid of finite depth is studied when the depth decreases over a finite interval
between liquids with constant depths to the left and right. The decrease in depth is specified by a parabolic function and
the pulse, which increases sharply in time and then decays, is turned on at the initial time some distance to the right of
the section with a variable depth.
A Laplace transform method is used to solve the corresponding initial value-boundary value problem and this makes it possible
to obtain a solution in hypergeometric functions in the transform space. In the limiting case of a linear variation in the
depth, a numerical inversion of the Laplace transform is used to construct solutions which are analyzed for various geometric
parameters and at different times.
Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya
Mekhanika, No. 29, pp. 131–142, 1999. |
