In this talk, it takes into account the KdV equation as an approximate model of long waves of small amplitude at the free surface with inviscid fluid. It is demonstrated that the mechanical balance quantities defined by the solution of the KdV equation are rigorously approximate in some appropriate space with the mechanical balance quantities in the context of Euler system and can be estimated in terms of the long wave of parameter.
https://indico.math.cnrs.fr/event/7009/