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On the Hierarchy of the Generalized KdV Equations

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Singular Limits of Dispersive Waves

Part of the book series: NATO ASI Series ((NSSB,volume 320))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA

    Carlos E. Kenig

  2. Department of Mathematics, University of California, 93106, Santa Barbara, CA, USA

    Gustavo Ponce

  3. Facultad de Ciencias, Universidad Autonoma de Madrid Cantoblanco, 28049, Madrid, Spain

    Luis Vega

Authors
  1. Carlos E. Kenig
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  2. Gustavo Ponce
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  3. Luis Vega
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Editor information

Editors and Affiliations

  1. University of Arizona, Tucson, Arizona, USA

    N. M. Ercolani  & C. D. Levermore  & 

  2. Landau Institute for Theoretical Physics, Moscow, Russia

    I. R. Gabitov

  3. Ecole Normale Superieure de Lyon, Lyon, France

    D. Serre

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© 1994 Springer Science+Business Media New York

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Kenig, C.E., Ponce, G., Vega, L. (1994). On the Hierarchy of the Generalized KdV Equations. In: Ercolani, N.M., Gabitov, I.R., Levermore, C.D., Serre, D. (eds) Singular Limits of Dispersive Waves. NATO ASI Series, vol 320. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2474-8_24

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  • DOI: https://doi.org/10.1007/978-1-4615-2474-8_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6054-4

  • Online ISBN: 978-1-4615-2474-8

  • eBook Packages: Springer Book Archive

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