On the Hierarchy of the Generalized KdV Equations
We consider a sequence of one-dimensional dispersive equations. These equations contain the KdV hierarchy as well as several higher order models arising in both physics and mathematics. We obtain conditions which guarantee that the corresponding initial value problem is locally and globally well-posed in appropiated function spaces. Our method is quite general and can be used to study other dispersive systems and related problems.
KeywordsSolitary Wave Initial Value Problem High Order Model Nonlinear Schrodinger Equation Water Wave Problem
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- W. Craig, T. Kappeler and W. A. Strauss, Gain of regularity for equations of KdV type, preprint, to appear in Ann. IHP, Analyse Nonlineaire.Google Scholar
- 3.T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Advances in Mathematics Supplementary Studies, Studies in Applied Math. 8 (1983), 93–128.Google Scholar
- 5.C. E. Kenig, G. Ponce and L. Vega, Small solutions to nonlinear Schrödinger equations, to appear in Ann. IHP, Analyse Nonlineaire.Google Scholar
- 6.C. E. Kenig, G. Ponce and L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle,preprint.Google Scholar
- 8.S. Kichenassamy and P. J. Olver, Existence and Non-existence of solitary waves solutions to higher order model evolution equations, preprint.Google Scholar
- 10.G. Ponce, Lax pairs and higher order models for water waves, to appear in J. Diff. Eqs.Google Scholar
- 14.L. Vega, Doctoral Thesis, Universidad Autonoma de Madrid, Spain (1987).Google Scholar