Ponce, Gustavo Lax pairs and higher order models for water waves. (English) Zbl 0796.35148 J. Differ. Equations 102, No. 2, 360-381 (1993). 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. Reviewer: L.Vazquez (Madrid) Cited in 44 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:uniqueness; locally well-posed; Lax pairs PDFBibTeX XMLCite \textit{G. Ponce}, J. Differ. Equations 102, No. 2, 360--381 (1993; Zbl 0796.35148) Full Text: DOI