Abstract
Bousssinesq-type equations are a powerful tool to model the wave propagation from intermediate waters to the shore. By construction, these equations have a good performance in weakly dispersive conditions, and a great effort has been done during the last 20 years to increase their range of application to deeper waters; the improved equations introduce free coefficients that are chosen for this purpose. Some of the improved sets of equations show instabilities when numerically solved over uneven beds. In this work we show how these instabilities can be due to the equations (including the values of the involved coefficients) and not to the numerical scheme. We further introduce new sets of coefficients that optimize the linear performance while improving the linear stability of the equations.
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