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arXiv · 1411.6709

On functional equations leading to exact solutions for standing internal waves

Felix Beckebanze·Grant Keady
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Abstract

The Dirichlet problem for the wave equation is a classical example of a problem which is not well-posed. Nevertheless, it has been used to model internal waves oscillating sinusoidally in time, in various situations, standing internal waves amongst them. We consider internal waves in two-dimensional domains bounded above by the plane z=0 and below by z=-d(x) for depth functions d. This paper draws attention to the Abel and Schr{ö}der functional equations as a convenient way of organizing analytical solutions. Exact internal wave solutions are constructed for a selected number of simple depth functions d.

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Felix Beckebanze, Grant Keady. 2014-11-25. On functional equations leading to exact solutions for standing internal waves. https://doi.org/10.1016/j.wavemoti.2015.09.009

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