Water waves and integrability.
Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymptotic expansion of Euler's equations is considered (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modelling the motion of shallow water waves are reviewed in this contribution.
Ivanov
Rossen I
RI
School of Mathematics, Trinity College Dublin, Dublin 2, Republic of Ireland. ivanovr@tcd.ie