TITLE

# Propagation of an initial N-wave in a bubbly fluid

AUTHOR(S)
Sandqvist, Henrik
PUB. DATE
July 2000
SOURCE
AIP Conference Proceedings;2000, Vol. 524 Issue 1, p513
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Propagation of sound in a bubbly fluid can, if dissipation is neglected, be described by Korteweg de Vries' equation. This can be solved with the inverse scattering transform. Korteweg de Vries' equation is studied as an initial value problem with an N-wave as initial condition. The inverse scattering method, leading to Marchenko's linear integral equation, is used, From the solution of Marchenko's equation the scattering potential, which also is the solution of Korteweg de Vries' equation, is obtained. In Marchenko's equation, the reflection coefficient of the scattering problem is found as a factor in two integrals. With an N-wave as initial condition, this reflection coefficient becomes non-zero and the two integrals are integrated numerically. To get the scattering potential, the Marchenko integral equation is solved by iteration. Already in the first step solution, the scattering potential at t = 0 coincides well with the given initial condition of the Korteweg de Vries equation, This solution decays quickly to the right of the front, which is moving to the right, and is oscillating and more slowly decaying to the left. By comparison with an asymptotic matching solution, the decay to the right can be shown to be exponential.
ACCESSION #
5665223

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