Lax pairs and higher order models for water waves (Q685795)

It is shown a local well-posedness result (in \(H^ s(\mathbb{R})\), \(s \geq 4)\) for a class of higher order nonlinear dispersive equations. The analysis is restricted to the model \[ u_ t + c_ 1 u_ xu_{xx} + c_ 2uu_{xxx} + c_ 3u_{xxxxx} = 0 \] which resembles the essential features of the next equation in the KdV hierarchy (beyond the KdV itself) and some models appearing in water wave problems.